Existence of infinitely many solutions for semilinear problems on exterior domains

Joseph Iaia

doi:10.3934/cpaa.2020193

Article Contents

2020, Volume 19, Issue 9: 4269-4284. Doi: 10.3934/cpaa.2020193

This issue Previous Article On nonexistence of extremals for the Trudinger-Moser functionals involving

$ L^p $

norms Next Article On special regularity properties of solutions of the benjamin-ono-zakharov-kuznetsov (bo-zk) equation

Existence of infinitely many solutions for semilinear problems on exterior domains

Joseph Iaia

University of North Texas, Denton, TX 76203-1430, USA

Received: August 31, 2019

Revised: February 29, 2020

Published: June 2020

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Abstract

In this paper we prove the existence of infinitely many radial solutions of $ \Delta u + K(r)f(u) = 0 $ on the exterior of the ball of radius $ R>0 $, $ B_{R} $, centered at the origin in $ {\mathbb R}^{N} $ with $ u = 0 $ on $ \partial B_{R} $ and $ \lim_{r \to \infty} u(r) = 0 $ where $ N>2 $, $ f $ is odd with $ f<0 $ on $ (0, \beta) $, $ f>0 $ on $ (\beta, \infty), $ $ f $ superlinear for large $ u $ and $ 0< K(r) \leq \frac{K_{1}}{r^{\alpha}} $ with $ 2<\alpha <2(N-1) $ for large $ r $.

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Mathematics Subject Classification: Primary: 34B40; Secondary: 35B05.

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