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Badiale, M. and Serra, E. (2010) Semilinear Elliptic Equations for Beginners: Existence Results via the Variational Approach. Springer Science and Business Media, London. https://doi.org/10.1007/978-0-85729-227-8

has been cited by the following article:

• TITLE: Pseudo-Index Theory for a Schrödinger Equation with Competing Potentials

  AUTHORS: Rui Sun

  KEYWORDS: Pseudo-Index, Multiplicity, Concentration, Sign-Changing Solution

  JOURNAL NAME: Open Access Library Journal, Vol.10 No.11, November 23, 2023

  ABSTRACT: In this paper, we study a nonlinear Schr?dinger equation with competing potentials -ε2Δν+V(x)ν=W1(x)|ν|p-2ν+W2(x)|ν|q-2ν, ν∈H1(RN), where ε>0, p,q∈(2,2*), p>q, , V(x), W1(x) and W2(x) are continuous bounded positive functions. Under suitable assumptions on the potentials, we consider the existence, concentration, convergence and decay estimates of the ground state solution for this equation. Furthermore, the multiplicity of semi-classical solutions is established by using Benci pseudo-index theory, and the existence of sign-changing solutions is obtained via Nehari method.