logical reasoning questions with solutions for clat

... [14] For instance, Messaoudi [11] studied (1.2) for h(ut) = a|ut|m utand f(u) = b|u|p-2uand proved a blow-up result for solutions with negative initial energy if p >m ≥ 2 and a global result for ... accommodate certain solutions with positive initial energy Song and Zhong [13] considered (1.2) for h(ut) = -Δutand f(u) = |u|p-2u and proved a blow-up result for solutions with positive initial ... of solutions for a system of nonlinear viscoelastic wave equations with strong damping Fei Liang1,2 and Hongjun Gao1* * Correspondence: gaohj@hotmail. com 1 Jiangsu Provincial Key Laboratory for

Ngày tải lên: 21/06/2014, 00:20

... Trang 1R E S E A R C H Open AccessPeriodic solutions for nonautonomous second order Hamiltonian systems with sublinear nonlinearity Zhiyong Wang1* and Jihui Zhang2 * Correspondence: ... article Abstract Some existence and multiplicity of periodic solutions are obtained for nonautonomous second order Hamiltonian systems with sublinear nonlinearity by using the least action principle ... measurable in t for every xÎ ℝNand continuously differentiable in x for a.e tÎ [0, T], and there exist a Î C(ℝ+ ,ℝ+ ), bÎ L1 (0, T ;ℝ+ ) such that |F(t, x)| ≤ a(|x|)b(t), |∇F(t, x)| ≤ a(|x|)b(t) for all

Ngày tải lên: 21/06/2014, 00:20

... Article ID 736093, 11 pagesdoi:10.1155/2011/736093 Research Article Three Solutions for Forced Duffing-Type Equations with Damping Term Yongkun Li and Tianwei Zhang Department of Mathematics, ... distinct solutions for the following resonant Duffing-type equations with damping and perturbed term ut  σut  ft, ut  λgt, ut  pt, a.e t ∈ 0, ω, u0  0  uω and without ... 20 cos2s  x 1/3 fors, x ∈ 0, 2π × −∞, −1, 20 cos2s  Q1x fors, x ∈ 0, 2π × −1, −0.001, 20 cos2s − x 1/3 fors, x ∈ 0, 2π × −0.001, 0.001, 20 cos2s  Q2x fors, x ∈ 0, 2π

Ngày tải lên: 21/06/2014, 05:20

... The existence of positive solutions for two above cases received wide attentionsee 3 10 For example, Ji and Ge 4 studied the multiplicity of positive solutions for the multipoint boundary ... ∅ and αTu > b for u ∈ Pγ, θ, α, b, c, d; S2 αTu > b for u ∈ Pγ, α, b, d with θTu > c; S3 0 / ∈ Rγ, ψ, a, d and ψTu < a for u ∈ Rγ, ψ, a, d with ψu  a. Then ... λu ≤ λψu for 0 ≤ λ ≤ 1, such that forpositive number M and d, for all u ∈ Pγ, d Suppose T : Pγ, d → Pγ, d is completely continuous and there exist positive numbers a, b, and c with a <

Ngày tải lên: 21/06/2014, 05:20

... of solutions for fourth-order boundary value problems with three parameters,” Mathematical and Computer Modelling, vol 46, no 3-4, pp 525–534, 2007 8 H Ma, “Symmetric positive solutions for ... theorem and operator spectral theorem, the existence of positive solutions for the nonlocal fourth-order boundary value problem with variable parameter u4t  Btut  λft, ut, ut, ... with Bt  β Since the parameters Bt is variable, we cannot expect to transform directly BVP1.2 into an integral equation as in16 We will apply the cone fixed point theory, combining with

Ngày tải lên: 21/06/2014, 07:20

... and lower solutions method together with maximal principle, we establish anecessary and sufficient condition for the existence of pseudo-C30, 1 as well as C20, 1 positive solutions for fourth-order ... 20 X Zhang and L Liu, “A necessary and sufficient condition for positive solutions for fourth-order multi-point boundary value problems with p-Laplacian,” Nonlinear Analysis: Theory, Methods & ... this paper, we consider the existence of positive solutions for the following nonlinear fourth-order singular p-Laplacian differential equations with integral boundary conditions:  ϕ p xt

Ngày tải lên: 21/06/2014, 11:20

... several 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 ... differential equations with three-point boundary conditions,” Computers & Mathematics with Applicationsl, vol 58, no 9, pp 1838–1843, 2009 16 Z Bai and H L ¨u, “Positive solutions for boundary value ... 10 pagesdoi:10.1155/2010/691721 Research Article Existence of Solutions for Nonlinear Fractional Integro-Differential Equations with Three-Point Nonlocal Fractional Boundary Conditions Ahmed

Ngày tải lên: 21/06/2014, 16:20

... +∞, λ, µ ∈ R. (A) For i = 1, 2, a i ∈ L r i (x) (Ω), a i (x) > 0 for x ∈ Ω, G i (x, u) is measurable with spect to x (for every u ∈ R) and locally Lipschitz with respect to u (for a.e x ∈ Ω), ... freely for any purposes (see copyright notice below) For information about publishing your research in Boundary Value Problems go to http://www.boundaryvalueproblems.com/authors/instructions/ For ... study the existence and multiplicity of solutions for the differential inclusion problem with singular coefficients involving the p(x)-Laplacian of the form where the following conditions are

Ngày tải lên: 21/06/2014, 17:20

... acceptance Fully formattedPDF and full text (HTML) versions will be made available soon Existence of positive solutions for fourth-order semipositone multi-point boundary value problems with a sign-changing ... freely for any purposes (see copyright notice below) For information about publishing your research in Boundary Value Problems go to http://www.boundaryvalueproblems.com/authors/instructions/ For ... solutions for multi-point boundary value problems has beenwidely studied in recent years For details, see [1–15] and references therein We note that the existence of n solutions and/or positive solutions

Ngày tải lên: 21/06/2014, 17:20

... upon acceptance Fully formattedPDF and full text (HTML) versions will be made available soon Positive solutions for boundary value problem for fractional differential equation with $p$-Laplacian ... et al investigated the existence of positive solutions for the nonlinear fractional boundary value problem (BVP for short) Trang 4Leggett-solutions for the following fractional BVPC D0+q u(t) ... value problems with p-Laplacian operator Trang 5However, there are few articles dealing with the existence of solutions to boundaryvalue problems for fractional differential equation with p-Laplacian

Ngày tải lên: 21/06/2014, 17:20

... 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 Science, Jiangxi ... 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 periodic solutions ... pin1.3 Since there is no concrete form for the p-Laplacian-like 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

Ngày tải lên: 21/06/2014, 18:20

... presents sufficient conditions for the existence and uniqueness of positive solutions for a discrete fourth-order beam equation under Lidstone boundary conditions with a parameter; the iterative ... ecology, and cybernetics, for details, see Trang 2 1 7and multiplicity of positive solutions of fourth-order problem, for example, 8 10 particular the discrete problem with Lidstone boundary conditions 11–17 ... solutions are also given The main tool used is monotone iterative technique 1 Introduction In this paper, we are interested in the existence, uniqueness, and iteration of positive solutions for

Ngày tải lên: 21/06/2014, 18:20

... 18 pagesdoi:10.1155/2009/312058 Research Article Existence of Positive Solutions for Multipoint Boundary Value Problem with p-Laplacian on Time Scales Meng Zhang,1 Shurong Sun,1 and Zhenlai Han1, ... Victoria Otero-Espinar We consider the existence of positive solutions for a class of second-order multi-point boundary value problem withp-Laplacian on time scales By using the well-known Krasnosel’ski’s ... 6, and so forth At the same time, motivated by the wide application of boundary value problems in physical and applied mathematics, boundary value problems for dynamic equations with p-Laplacian

Ngày tải lên: 21/06/2014, 20:20

... appeared upon acceptance Fully formattedPDF and full text (HTML) versions will be made available soon. L^{\infty} estimates of solutions for the quasilinear parabolic equation with nonlinear gradient ... freely for any purposes (see copyright notice below). For information about publishing your research in Boundary Value Problems go to http://www.boundaryvalueproblems.com/authors/instructions/ For ... of the assumed solutions u(t) and give a proof of Theorem 2.4 The solutions are in fact given as limits of smooth solutions of appropriate approx-imate equations and we may assume for our estapprox-imates

Ngày tải lên: 21/06/2014, 20:20

... problems with nonlinearity f being nonnegative on time scales Therefore, it is a natural problem to consider the existence of positive solution for higher order p-Laplacian equations with sign ... that it exists, with the property that for each  > 0, there is a neighborhood U of t such that  fσt − fs − fΔtσt − s ≤ |σt − s| 2.2 for all s ∈ U. For f : T → R and ... difficult to find positive solutions of the p-Laplacian equation when the nonlinearity changes sign In particular, little work has been done on the existence of positive solutions for higher order p-Laplacian

Ngày tải lên: 21/06/2014, 20:20

... φ1σ ∈ K for each σ ∈ R Now from the uniform continuity of F bon bounded subsets ofX, it obviously follows that F bis uniformly continuous on K uniformly for each t ∈ R Therefore for every ε ... Ft, u with F·, u ∈ L p locR; X for each u ∈ Y, is said to be Sp -almost automorphic in t ∈ R uniformly in u ∈ Y if t → Ft, u is S p -almost automorphic for each u ∈ Y; that is, for every ... b  ϕ b Moreover,λf b  λf b for each scalar λ. Definition 2.3 The Bochner transform F b onR × X, with values in X, is defined by F b t, s, u : Ft  s, u for each u ∈ X. Definition 2.4

Ngày tải lên: 21/06/2014, 20:20

... Article Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum Ruyun Ma and Chenghua Gao College of Mathematics and Information Science, Northwest ... equations with nonlinear boundary conditions Our ideas arise from 1, 3 In 1993, Brykalov 1 discussed the existence of two different solutions to the nonlinear differential equation with nonlinear ... x| ≤ in2 From 1,2 , it is clear that the results of 1 are valid for functional differential equations in general form and for some cases of unbounded right-hand side of the equationsee 1,

Ngày tải lên: 22/06/2014, 11:20

... conditions that this system does not have solutions satisfying the con-ditionu1(t)u2(t) < 0 for t∈[t0, +∞) Note one of our results obtained for this systemwith constant coefficients and delays (p(t)≡ ... necessary and sufficient for nonexistence of solutions satisfying the Trang 3condition (1.4) It is clear that the inequality√pδ > 2/e is necessary and sufficient for nonexistence of solutions satisfying ... thatϕ(t) = ϕ(t ∗) fort ∈[t∗,t∗] andϕ(t ∗)= ϕ(t ∗) On the other hand, sinceψ is a nonincreasing function, we haveψ(t)ϕ(t) ≥ ψ(t ∗)ϕ(t∗) fort ∈[t0,t∗] Thereforet ∗ ∈ E1∩ E2 By theabove reasoning we

Ngày tải lên: 22/06/2014, 18:20

... considered the existence of weak solutions for differential inclusions of various forms Miettinen [6] Miettinen and Panagiotopoulos [7] proved the existence of weak solutions for some parabolic differential ... k,p( Ω) For simplicity, we denote · 2by ·  For every q ∈(1,∞), we denote the dual ofW01,qbyW −1,q withq  = q/(q −1) The notation (·,·) for theL2-inner product will also be used for the ... study the existence of global weak solutions for a hyperbolic differential inclusion with a source term, and then investigate the asymptotic stability of the solutions by using Nakao lemma Copyright

Ngày tải lên: 22/06/2014, 18:20

... α0+α1y(1) for t ∈[−τ,0], y(t) ≥ β1− β0 β1(T + 1) yfort ∈[1,T + 2]  . (2.8) ThenE is a Banach space endowed with norm  · andK is a cone in E. Fory ∈ K, we have y(t) =(α1/(α0+α1))y(1) for t ∈[−τ,0] ... one of the following two conditions: (1) Ψx x for x ∈ K ∩ ∂Ω1,  Ψx  ≥ x for x ∈ K ∩ ∂Ω2; (2) Ψx x for x ∈ K ∩ ∂Ω2,  Ψx  ≥ x for x ∈ K ∩ ∂Ω1. Then Ψ has a fixed point in K ∩(Ω2\Ω1). ... existence of positive solutions for boundary value problems of nonlinear functional difference equations with p-Laplacian operator is investigated Sufficient conditions are obtained for the existence

Ngày tải lên: 22/06/2014, 19:20