Discrete boundary value problems have been discussed extensively in the literature; see, for example, Agarwal et al. [1], Anderson et al. [5], and Avery et al. [6], as well as the references cited therein. In [1], the authors use critical point theory to establish the existence of multiple solutions of some regular as well as singular discrete boundary value problems. Solvability of a nonlinear...

A static mixed boundary value problem of physically nonlinear elasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary linear operator, a non-standard boundary-domain integro-differential formulation of the problem is presented, with respect to the displacements and their gradients. Using a cut-off fu...

which is a discrete analogue of the Neumann problem about the rotationally symmetric spacelike graphs with a prescribed mean curvature function in some Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, whereψ (s) := ∫ s 0 dt g(t) ,ψ –1 is the inverse function ofψ , and H :R× [2,N – 1]Z →R is continuous with respect to the first variable. The proofs of the main results are based upon the Br...

and Applied Analysis 3 Ma and Xu 15 also applied the fixed point theorem in cones to obtain some results on the existence of generalized positive solutions. It is the purpose of this paper to show some new results on the existence and multiplicity of generalized positive solutions of 1.4 , 1.8 by Dancer’s global bifurcation theorem. To wit, we get the following. Theorem 1.3. Let h : 2 → 0,∞ , f...

Various generalizations of the Gronwall inequality 1, 2 are fundamental tools in the study of existence, uniqueness, boundedness, stability, invariant manifolds, and other qualitative properties of solutions of differential equations and integral equation. There are a lot of papers investigating them such as 3–8 . Along with the development of the theory of integral inequalities and the theory ...