exact similarity solutions of nonlinear pdes

... the existence of one-sign solutions of the nonlinear problem x ft, x, t ∈ 0, T, x 0  xT, x0  xT. 1.18 The proofs of the main results are based on the properties of G and the ... existence of positive solutions of 3.17 will not be guaranteed in this case Proof of Theorem 3.2 We only provei ii can be proved by a similar method To study the existence of positive solutions ... result concerning the global structure of the set of positive solutionsof parameterized nonlinear operator equations, which is essentially a consequence of Dancer 12, Theorem 2 Suppose thatE...

Ngày tải lên: 21/06/2014, 11:20

... introduced by Ishii 5 in Trang 2the proof of existence of viscosity solutions of first-order Hamilton-Jacobi equations, Crandallet al had applications of Perron’s Method to second-order partial ... Hamilton-Jacobi equations to nonlinear parabolic equations, then by using Perron’s method to study the existence and uniqueness of time almost periodic viscosity solutions of nonlinear parabolic equations ... periodic and almost periodic viscosity solutions of first-order Hamilton-Jacobi equations Nunziante considered the existence and uniqueness of viscosity solutions of parabolic equations with discontinuous...

Ngày tải lên: 21/06/2014, 20:20

... Existence Theorems of Multiple Positive Solutions of Nonlinear m-Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales 1 Department of Mathematics, North University of China, Taiyuan, ... at least two positive solutions u1and u2. Motivated by the above papers, the purpose of our paper is to show the existence of twin or an arbitrary odd number of positive solutions to the BVP 1.1, ... the existence of positive solutions for second-order nonlinear boundary value problems on time scales, for examples, see1 6 and references therein At the same time, multipoint nonlinear boundary...

Ngày tải lên: 21/06/2014, 20:20

... solution of 2.7 for n ≥ 1. Remark 3.3 Recently Song4 obtained a more general result than that ofTheorem 3.2, that is, under the assumption of asymptotic almost periodicity of a bounded solution of2.7, ... Mariella Cecchi We study the existence of almost periodic solutions for nonlinear discrete Volterra equations with unbounded delay, as a discrete analogue of the results for integro-differential ... Also, he showed the existence of an almost periodic solution under the assumption of total stability in2 Song and Tian3 studied periodic and almost periodic solutions of discrete Volterra equations...

Ngày tải lên: 22/06/2014, 11:20

... that operator (2.29) is nonlinear 3 Mutual comparability of solutions of ( 1.1 ) The aim of this section is to establish certain conditions under which each two solutions of (1.1) lying in a certain ... interior of the abovementioned cone in L ∞[0, 1] is empty The proofs of the results of this paper rely upon properties of a certain nonlinear tional associated with the wedgeK and a certain suitably ... exam-ple of a pair of nonlinear operators possessing the properties indicated is provided by thepositive and negative parts of a function Example 2.17 Let X : = C([0,1],R) be the space of the continuous...

Ngày tải lên: 22/06/2014, 18:20

... Received 6 August 2004 We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t)= f (y(t)), where c
=0 ... extend previous ones of Etheridge and Rodriguez [4] who studied the existence of periodic solutions of difference equations under signifi-cantly more restrictive conditions on the nonlinearities 2 ... Ψ(N), whence the columns of Ψ( ·) lie inX N One then observes that, just as the dimension of ker(L) is equal to that of ker(I − A N), the dimension of ker(L) is equal to that of ker(I −(A − T)N)...

Ngày tải lên: 23/06/2014, 00:20

... analysis of the positivity of solutions and the establishment of the exponential stability conditions for the positive equilibrium of such systems.This study addresses the positivity of solutions ... attempt devoted to the study of positive nonlinear systems in neural networks For neural systems, the nonlinearity of neuron activation functions makes the study of positive neural networks more ... investigates the positivity of solutions and exponential stability of positive equilibrium in nonlinear differential equations with delays, focusing on various types of neural networks The main...

Ngày tải lên: 31/07/2024, 16:30

... Trang 1MINISTRY OF EDUCATION AND TRAININGHANOI NATIONAL UNIVERSITY OF EDUCATION ——————–o0o——————— LE THI HONG DUNG STABILITY OF POSITIVE SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS ... positive solutions and stability of nonlinear differential equations withdelays B Research aims The thesis focuses on problems of stability of several classes of nonlinear positive ential systems ... is concerned with the positivity of solutions and exponential stability ofpositive equilibrium of nonlinear differential equations with delays in various types of neuralnetworks Main contribution...

Ngày tải lên: 31/07/2024, 17:01

... condition for theboundedness of all solutions of (1.1) and the scalar case of (1.1), respectively The next result provides a sufficient condition for the boundedness of solutions of (1.1) Theorem 4.1 ... boundedness of the solutions in nonlinear discrete Volterra difference equationsIstv´an Gy˝ori∗1 and Essam Awwad1,2 1 Department of Mathematics, Faculty of Information Technology, University of Pannonia, ... have proved that thesolutions of the discrete linear Volterra equation converge to a finite limit, which in general is non-trivial.The main result on the boundedness of solutions of a linear Volterra...

Ngày tải lên: 20/06/2014, 20:20

... properly cited. Trang 2Existence of positive solutions for nonlinearm-point boundary value problems on time scales 1 School of Mathematics and Physics, China University of Geosciences, Beijing 100083, ... value problems of ordinary differential equations (BVPs for short)arise in a variety of different areas of applied mathematics and physics For example, thevibrations of a guy wire of a uniform ... and composed of N parts of differentdensities can be set up as a multi-point boundary value problem [3] Many problems in thetheory of elastic stability can be handled by the method of multi-point...

Ngày tải lên: 20/06/2014, 20:20

... and the uniqueness of the solution of problem (1.1), whose proof can be found in Han and Wang [19] (Theorem 2.1) with slight modification, so we will omit its proof In the proof, the authors adopted ... Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China Full list of author information is available at the end of the article ... exponential or polynomial decay of the solutions energy, depending on the decay rate of the relaxation functions g(s) and h(s) For the problem (1.1) inℝn , we mention the work of Kafini and Messaoudi...

Ngày tải lên: 21/06/2014, 00:20

... a large number of papers dealing with the existence of solutions of nonlinear fractional differential equations by the use of techniques of nonlinear analysis (fixed point theorems, Leray-Schauder ... School of Science, University of Jinan, Jinan 250022, Shandong, PR China Full list of author information is available at the end of the article Abstract In this article, we study the existence of ... works above, in this article we investigate the existence of positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders ⎧ ⎪ ⎪ −D α 0 +u(t) = f (t, v(t)),...

Ngày tải lên: 21/06/2014, 03:20

... Research Article Existence of Solutions to Nonlinear Langevin Equation Involving Two Fractional Orders with Boundary Value Conditions Anping Chen1, and Yi Chen2 Department of Mathematics, Xiangnan ... Province, and the Construct Program of the Key Discipline in Hunan Province References A Alsaedi, “Existence of solutions for integrodifferential equations of fractional order with antiperiodic ... conditions,” International Journal of Differential Equations, vol 2009, Article ID 417606, pages, 2009 B Ahmad, “Existence of solutions for fractional differential equations of order q ∈ 2, with antiperiodic...

Ngày tải lên: 21/06/2014, 05:20

... papers 1 3, 11–14, the authors studied the existence of periodic solutions, subharmonic solutions, and homoclinic solutions of some special forms of1.1 by using the critical point theory These ... pagesdoi:10.1155/2010/470375 Research Article Existence of Homoclinic Solutions for a Class of Nonlinear Difference Equations Peng Chen and X H Tang School of Mathematical Sciences and Computing Technology, ... to the study of periodic solutions for difference equations Along this direction, Ma and Guo13 applied the critical point theory to prove the existence of homoclinic solutions of the following...

Ngày tải lên: 21/06/2014, 11:20

... fromλ1a0, λ1a0 × {0} in R × E. 3 Proof of the Main Results Proof of Theorem 1.5 It is clear that any solution of2.30 of the form 1, u yields solutions u of1.1 We will show that C crosses ... singularities at t  0, 1 The proof of our main result is based upon topological degree theory and global bifurcation techniques 1 Introduction Existence and multiplicity of solutions of singular problem ... the method of lower and upper solutions, Leray-Schauder continuation theorem, and the fixed point index Trang 2theory in cones Recently, Ma 7 studied the existence of nodal solutions of the singular...

Ngày tải lên: 21/06/2014, 11:20

... researchers with the sphere of study ranging from the theoretical aspects of existence and uniqueness of solutions to the analytic and numerical methods for finding solutions For some recent work ... uniqueness of mild solutions to impulsive fractional differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol 72, no 3-4, pp 1604–1615, 2010. 11 B Ahmad, “Existence of solutions ... Article Existence of Solutions for Nonlinear Fractional Integro-Differential Equations with Three-Point Nonlocal Fractional Boundary Conditions Ahmed Alsaedi and Bashir Ahmad Department of Mathematics,...

Ngày tải lên: 21/06/2014, 16:20

... For an introduction of the basic theory of impulsive differential equations, see Lakshmikantham et al 1; for an overview of existing results and of recent research areas of impulsive differential ... obtained the existence of positive solutions by means of fixed point index theory Recently, Yang and Wei 23 and the author of 24 improved and generalized the results of Pang et al.22 by ... investigating the existence of positive solutions of nth impulsive differential equations by using the fixed point theorem of cone expansion and compression The objective of the present paper is to...

Ngày tải lên: 21/06/2014, 16:20

... Article Existence and Uniqueness of Periodic Solutions for a Class of Nonlinear Equations with p-Laplacian-Like Operators Hui-Sheng Ding, Guo-Rong Ye, and Wei Long College of Mathematics and Information ... uniqueness of periodic solutions for a kind of Lienard type p-Laplacian equation, Nonlinear Analysis TMA, 69, 724–729, 2008 1 Introduction In this paper, we deal with the existence and uniqueness of ... operator ϕ of 1.1, it is more difficult to prove the existence of periodic solutions to 1.1 Therefore, in this paper, we will devote ourselves to investigate the existence of periodic solutions...

Ngày tải lên: 21/06/2014, 18:20

... Journal of Mathematical Analysis and Applications, vol 291, no 1, pp 352–367, 2004 10 R Ma and N Castaneda, “Existence of solutions of nonlinear m-point boundary-value problems,” Journal of Mathematical ... positive solutions of BVP 1.2 The main features of the present paper are as follows Firstly, compared with , the problem we discussed here is systems of multipoint boundary value problem and nonlinear ... Then the conclusion of Theorem 3.2 holds Proof The proof is almost the same as that of Theorem 3.2 The only difference is that, instead is implied directly by 3.15 and 3.16 , of using condition...

Ngày tải lên: 21/06/2014, 20:20

... solvability of a nonlinear integral equation of Urysohn type Using the technique of measures of noncompactness we prove that under certain assumptions this equation possesses solutions that are convex of ... by virtue of2.5 ByC7 andTheorem 2.2we conclude the existence of at least one fixed point of F in Q This fixed point is obviously a solution of1.1 which in view of the definition of Q is ... Introduction Existence of solutions of differential and integral equations is subject of numerous investigationssee, e.g., the monographs 1 3 or 4 Moreover, a lot of work in this domain...

Ngày tải lên: 21/06/2014, 20:20