On Some Scalar Field Equations with Competing Coefficients

Abstract This paper deals with semilinear elliptic problems of the type {−Δu+α(x)u=β(x)|u|p−1uin RN,u(x)>0in RN,u∈H1(RN),  where $p$ is superlinear but subcritical and the coefficients $\alpha$ and $\beta$ are positive functions such that $\alpha(x) \to a_\infty > 0$ and $\beta(x)\to b_\infty...

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Bibliographic Details
Published in:International mathematics research notices 2018-04, Vol.2018 (8), p.2481-2507
Main Authors: Cerami, Giovanna, Pomponio, Alessio
Format: Article
Language:English
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Summary:Abstract This paper deals with semilinear elliptic problems of the type {−Δu+α(x)u=β(x)|u|p−1uin RN,u(x)>0in RN,u∈H1(RN),  where $p$ is superlinear but subcritical and the coefficients $\alpha$ and $\beta$ are positive functions such that $\alpha(x) \to a_\infty > 0$ and $\beta(x)\to b_\infty > 0$, as $|x| \to \infty$. Aim of this work is to describe some phenomena that can occur when the coefficients are “competing.”
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnw315