The existence of positive solution to some asymptotically linear elliptic equations in exterior domains
type: Item
instance of: scholarly article
title: The existence of positive solution to some asymptotically linear elliptic equations in exterior domains
zbMATH Open document ID: 1134.35038
DOI: 10.4171/RMI/466
author: Gongbao Li
author: Gao-Feng Zheng
published in: Revista Matemática Iberoamericana
publication date: 2007-05-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1161871348
full work available at URL: https://eudml.org/doc/41984
review text: Summary: We are concerned with the asymptotically linear elliptic problem \(-\Delta u+ \lambda_{0}u=f(u)\), \(u\in H_{0}^{1}(\Omega ) \) in an exterior domain \(\Omega= \mathbb{R}^{N}\setminus \overline{\mathcal O}\) \(( N\geqslant 3)\) with \({\mathcal O}\) a smooth bounded and star-shaped open set, and \(\lim_{t\rightarrow +\infty }\frac{ f(t)}{t}=l\), \(0<l<+\infty\). Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 5152583
zbMATH Keywords: asymptotically linear elliptic
zbMATH Keywords: exterior domain
zbMATH Keywords: algebraic topology argument
zbMATH Keywords: positive solution
MaRDI profile type: Publication
cites work: Dual variational methods in critical point theory and applications
cites work: On the existence of a positive solution of semilinear elliptic equations in unbounded domains
cites work: Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
cites work: Positive solutions of some nonlinear elliptic problems in exterior domains
cites work: Nonlinear scalar field equations. I: Existence of a ground state
cites work: Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
cites work: Solutions of asymptotically linear operator equations via morse theory
cites work: Q3999077
cites work: On the exterior Dirichlet problem for \(\Delta u-u+f(x,u)=0\)
cites work: On a class of asymptotically linear elliptic problems in \(\mathbb R^N\)
cites work: On the existence of positive entire solutions of a semilinear elliptic equation
cites work: Q3923023
cites work: Q4173739
cites work: On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝN
cites work: Uniqueness of the positive solution of \(\Delta u+f(u)=0\) in an annulus
cites work: Q4466542
cites work: The existence of a positive solution to asymptotically linear scalar field equations
cites work: Asymptotically linear Dirichlet problem for the \(p\)-Laplacian
cites work: MULTIPLE SOLUTIONS TO p-LAPLACIAN PROBLEMS WITH ASYMPTOTIC NONLINEARITY AS up−1 AT INFINITY
cites work: Q5749694
cites work: The concentration-compactness principle in the calculus of variations. The locally compact case. II
cites work: Existence of solitary waves in higher dimensions
cites work: Applying the mountain pass theorem to an asymptotically linear elliptic equation on RN
cites work: Positive solutions of semilinear elliptic problems in exterior domains
cites work: Positive solution for a semilinear elliptic equation which is almost linear at infinity
OpenAlex ID: W2058124266
description: scientific article; zbMATH DE number 5152583