Infinitely many solutions for nonlinear Schrödinger equations with electromagnetic fields

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

existence of infinitely many solutions for coupled system of schrödinger-maxwell's equations

Infinitely Many Periodic Solutions of Nonlinear Wave Equations on S

The existence of time periodic solutions of nonlinear wave equations utt −∆nu + ` n− 1 2 ́2 u = g(u)− f(t, x) on n-dimensional spheres is considered. The corresponding functional of the equation is studied by the convexity in suitable subspaces, minimax arguments for almost symmetric functional, comparison principles and Morse theory. The existence of infinitely many time periodic solutions is o...

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 Nonlinear Equations with Non-symmetric Potentials

We consider the following nonlinear Schrödinger equation { ∆u− (1 + δV )u + f(u) = 0 in R , u > 0 in R , u ∈ H(R ) where V is a continuous potential and f(u) is a nonlinearity satisfying some decay condition and some non-degeneracy condition, respectively. Using localized energy method, we prove that there exists a δ0 such that for 0 < δ < δ0, the above problem has infinitely many positive solu...