Multiplicity Results for some Nonlinear¶Schrödinger Equations with Potentials

On a “Zero Mass” Nonlinear Schrödinger Equation

“…This paper has been motivated by some well known works, such as [2,3,15,16,17,18,22,23,25,27,28], where the nonlinear Schrödinger equation…”

Singularly perturbed Neumann problems with potentials

“…Theorem 1.1 will be proved as a particular case of two multiplicity results in Section 6, where we will prove also Theorem 1.2. The proof of the theorems relies on a finite dimensional reduction, precisely on the perturbation technique developed in [1,2,3]. In Section 2 we give some preliminary lemmas and some estimates which will be useful in Section 3 and Section 4, where we perform the Liapunov-Schmidt reduction, and in Section 5, where we make the asymptotic expansion of the finite dimensional functional.…”

Multiscale-bump standing waves with a critical frequency for nonlinear Schrödinger equations

“…Their method, based on an interesting Lyapunov-Schmidt finite dimensional reduction, was extended by Oh in [28,29] to include a similar result in higher dimensions, provided 1 < p < N +2 N −2 . Other existence results for positive solutions of problem (1.2) under the condition inf x∈R N W (x) > E can be found in [1,2,3,10,12,13,14,15,16,17,20,22,24,25,27,31,32].…”