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In this article we study discrete nonlinear Schrodinger equations without periodicity assumptions. We show the existence of multiple solutions of the form $u_n e^{-i\omega t}$ (called breathers) by using Clark's Theorem in critical point theory.

This article concerns a second-order nonlinear difference equation. By using critical point theory, the existence of two heteroclinic orbits is obtained. The main method used is variational.

The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. In this article, we consider a class of discrete nonlinear Schrodinger equations with unbounded potentials. We obtain some new sufficient conditions on the multiplicity results of ground state solutions for the equations by using the symmetric mountain pass lemma. Recent results in the literature are greatly improved.

By using critical point theory, we prove the existence of a nontrivial homoclinic orbit for a class of nonlinear functional difference equations. Our conditions on the nonlinear term do not need to satisfy the well-known global Ambrosetti-Rabinowitz superquadratic condition.

By using the Mountain Pass Lemma, we establish sufficient conditions for the existence of solitons for the discrete nonlinear Schrodinger equations.

We establish existence criteria for homoclinic orbits of second-order nonlinear difference equations by using the critical point theory in combination with periodic approximations.

Using critical point theory, we obtain criteria for the existence and multiplicity of periodic and subharmonic solutions to fourth-order p-Laplacian difference equations. The proof is based on the Linking Theorem in combination with variational technique. Recent results in the literature are generalized and improved.