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2020 Existence of solutions for a nonhomogeneous Kirchhoff-Schrödinger type equation in $\mathbb{R}^{2}$ involving unbounded or decaying potentials
Francisco S.B. Albuquerque, Anouar Bahrouni, Uberlandio B. Severo
Topol. Methods Nonlinear Anal. 56(1): 263-281 (2020). DOI: 10.12775/TMNA.2020.013

Abstract

In this paper, we consider the following nonhomogeneous Kirchhoff-Schrödinger equation: $$ m\bigg(\int_{\mathbb{R}^{2}}|\nabla u|^2\,{d}x +\int_{\mathbb{R}^{2}}V(|x|)u^2\,{d}x \bigg) [-\Delta u + V(|x|)u] = Q(|x|)f(u) + \varepsilon h(x), $$ for $ x\in\mathbb{R}^2$, where $m$, $ V$, $ Q$ and $f$ are continuous functions, $\varepsilon$ is a small parameter and $h\neq 0$. When $f$ has exponential growth by means of a Trudinger-Moser type inequality, the Mountain Pass Theorem and Ekeland's Variational Principle in weighted Sobolev spaces are applied in order to establish the existence of at least two weak solutions for this equation.

Citation

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Francisco S.B. Albuquerque. Anouar Bahrouni. Uberlandio B. Severo. "Existence of solutions for a nonhomogeneous Kirchhoff-Schrödinger type equation in $\mathbb{R}^{2}$ involving unbounded or decaying potentials." Topol. Methods Nonlinear Anal. 56 (1) 263 - 281, 2020. https://doi.org/10.12775/TMNA.2020.013

Information

Published: 2020
First available in Project Euclid: 16 October 2020

MathSciNet: MR4175079
Digital Object Identifier: 10.12775/TMNA.2020.013

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.56 • No. 1 • 2020
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