[PDF] Top 20 Eigenvalue Problems for Laplacian Functional Dynamic Equations on Time Scales

... nonlinear functional dynamic equation on a time scale and obtained sufficient conditions for the existence of positive solutions, Li and Liu 10 studied the eigenvalue problem for second-order ... See full document

... nonlinear functional dynamic equation on time scales and obtained sufficient conditions for the existence of positive ...p-Laplacian functional dynamic equations on ... See full document

... value problems on time scales [–] since the theory of dynamic equations on time scales has been a new important mathematical branch (see, for example, [– ... See full document

... p-Laplacian problems with two-, three-, m-point boundary conditions for ordinary differential equations and finite difference equations have been studied extensively, for example see 1–4 and ... See full document

... namic equations on time scales (see, ...to eigenvalue problems for systems of nonlinear boundary value problems on time ... See full document

... Any arbitrary nonempty closed subset of the reals R can serve as a time-scale T ; see [9, 10]. For t ∈ T define the forward jump operator σ : T → T by σ (t) = inf { s ∈ T : s > t } , and the backward jump ... See full document

... (a) Let T be a time scale, that is, T is a closed subset of R . We assume that T has the topology that it inherits from the standard topology on R . Throughout, for any a,b (> a), the interval [a, b] is defined ... See full document

... Our problem is a dynamic analog of the BVPs 1.1 and 1.2. But it is more general than them. Moreover, conditions for the existence of at least one positive solution were studied for the BVPs 1.1 and 1.2. In this ... See full document

... p-Laplacian dynamic equations on time scales, see ...value problems for nonlinear p-Laplacian dynamic equations on time scales have not been ... See full document

... of dynamic equations on time scales was introduced firstly by Stefan Hilger in ...the time scale theory can not only unite continuous and discrete dynamic equa- tions but also ... See full document

... impulsive functional dynamic equa- tions on almost periodic time scales, we established several theorems in the paper (see Sections  and ) to obtain some new existence results for ...tional ... See full document

... of dynamic equations on time scales goes back to Stefan Hilger ...p-Laplacian problems on time scales; see, for example, ...value problems (BVP) for ... See full document

... p-Laplacian dynamic equations on time scales by means of the Avery-Henderson fixed point theorem and the five functionals fixed point ...nontrivial dynamic equation on specific ... See full document

... φ-Laplacian dynamic equation coupled with nonlinear boundary functional conditions that include as a particular case the Dirichlet and multipoint ... See full document

... concave functional on P, and let ψ be a nonnegative continuous functional on P satisfying ψλx ≤ λψx for 0 ≤ λ ≤ 1, such that for some positive numbers M and ... See full document

... differential equations, difference equations, dynamic equations on time scales, p-Laplacian, fractional order differential equations and boundary value ... See full document

... a time scale defined as the real numbers set, and in the second one, the existence of extremal solutions to PBVP ...a time scale defined as a sequence of discrete points union a closed real interval is ... See full document

... Note that V = V (x) and even if the vector field associated with the dynamic equation is autonomous, ˙ V still depends on t (and x of course) when the graininess function of T is nonconstant. Several formulas are ... See full document

... Exponential decay and stability of solutions of dynamic equations on time scales were investigated in recent papers [1, 5–7, 11, 12] using Lyapunov’s method. We use different approaches based ... See full document

... of dynamic equations on time scales was introduced by Stefan Hilger in  [], in order to unify continuous and discrete calculus [, ...A time scale T is a nonempty closed subset of ... See full document