Keywords: Discrete Homological nontrivial critical point Morse theory Local linking a b s t r a c t In this paper, the existence and multiplicity results of solutions are obtained for the discrete nonlinear two point boundary value problem (BVP) ÀD 2 uðk À 1Þ ¼ kf ðk; uðkÞÞ k 2 þ is a parameter. By using the critical point theory and Morse theory, we obtain that the above (BVP) has solutions fo...

this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.

Keywords: Difference equations Boundary value problems Symmetric Green's function Fixed points Fourth-order Discrete Beam Lidstone Semipositone a b s t r a c t Various existence, multiplicity, and nonexistence results for nontrivial solutions to a non-linear discrete fourth-order Lidstone boundary value problem with dependence on two parameters are given, using a symmetric Green's function appr...

We consider the inverse boundary value problem in the case of discrete electrical networks containing nonlinear (non-ohmic) conductors. For a fixed nonlinear electrical network, we show that under reasonable assumptions, there are well-defined Dirichletto-Neumann and Neumann-to-Dirichlet maps relating boundary voltages and boundary currents. We also generalize work of Curtis, Morrow, and others...