Infinitely Many Solutions for Cubic Nonlinear Schrödinger Equations in Dimension Four

A VARIATIONAL APPROACH TO THE EXISTENCE OF INFINITELY MANY SOLUTIONS FOR DIFFERENCE EQUATIONS

The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...

Infinitely Many Positive Solutions for the Nonlinear Schrödinger Equations in R

We consider the following nonlinear problem in R

New Exact Analytic Solutions for Stable and Unstable Nonlinear Schrödinger Equations with a Cubic Nonlinearity

The Exp-Function method is used for constructing new exact analytic solutions of stable and unstable nonlinear Schrödinger (SNLS and UNLS) equations with a cubic nonlinearity. The obtained solutions has not appeared in literature as far as we know. It is shown that many previous known results can be recovered as special cases of our results. Mathematics Subject Classification: 35C07, 35G20, 35Q55

Nonlinear Fractional Schrödinger Equations in One Dimension

We consider the question of global existence of small, smooth, and localized solutions of a certain fractional semilinear cubic NLS in one dimension, i∂tu − Λu = c0|u| 2 u + c1u 3 + c2uu 2 + c3u 3 , Λ = Λ(∂x) = |∂x| 1 2 , where c0 ∈ R and c1, c2, c3 ∈ C. This model is motivated by the two-dimensional water wave equation, which has a somewhat similar structure in the Eulerian formulation, in the...

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations