Existence of nontrivial solutions for perturbed elliptic system in \(\mathbb{R}^N\)
type: Item
instance of: scholarly article
title: Existence of nontrivial solutions for perturbed elliptic system in \(\mathbb{R}^N\)
zbMATH Open document ID: 1472.35134
DOI: 10.1155/2014/252438
author: Juan Jiang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We consider the perturbed nonlinear elliptic system \(- \varepsilon^2 \Delta u + V(x) u = K(x) | u |^{2^* - 2} u + H_u(u, v)\), \(x \in \mathbb{R}^N\), \(- \varepsilon^2 \Delta v + V(x) v = K(x) | v |^{2^* - 2} v + H_v(u, v)\), \( x \in \mathbb{R}^N\), where \(N \geq 3\), \(2^* = 2 N /(N - 2)\) is the Sobolev critical exponent. Under proper conditions on \(V\), \(H\), and \(K\), the existence result and multiplicity of the system are obtained by using variational method provided \(\varepsilon\) is small enough.
Mathematics Subject Classification ID: 35J47
Mathematics Subject Classification ID: 35J61
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 7022007
zbMATH Keywords: perturbed nonlinear elliptic system
zbMATH Keywords: existence, variational methods
Wikidata QID: Q59036942
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/252438
OpenAlex ID: W2053781741
cites work: Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
cites work: Semi-classical states for nonlinear Schrödinger equations
cites work: Multi-peak bound states for nonlinear Schrödinger equations
cites work: On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential
cites work: On an electromagnetic Schrödinger equation with critical growth
cites work: Multi-peak periodic semiclassical states for a class of nonlinear Schrödinger equations
cites work: Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions
cites work: Semiclassical states of nonlinear Schrödinger equations
cites work: Multiplicity results for some nonlinear Schrödinger equations with potentials
cites work: Local mountain-pass for a class of elliptic problems in \(\mathbb R^N\) involving critical growth
cites work: On existence and concentration behavior of ground state solutions for a class of problems with critical growth.
cites work: Solutions of perturbed Schrödinger equations with critical nonlinearity
cites work: Solutions of perturbed Schrödinger equations with electromagnetic fields and critical nonlinearity
cites work: Existence and concentration of positive solutions for a class of gradient systems
cites work: Existence of Solution for a Class of Quasilinear Systems
cites work: On Existence and Concentration of Solutions for a Class of Hamiltonian Systems in ℝN
cites work: On the existence and shape of least energy solutions for some elliptic systems.
cites work: Critical point theory and Hamiltonian systems
cites work: On Critical Point Theory for Indefinite Functionals in The Presence of Symmetries
description: scientific article; zbMATH DE number 7022007