Thresholds for the existence of solutions to inhomogeneous elliptic equations with general exponential nonlinearity

Kazuhiro Ishige, Shinya Okabe, Tokushi Sato

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1 Citation (Scopus)

Abstract

In this paper we study the existence and the nonexistence of solutions to an inhomogeneous non-linear elliptic problem -Δu+u=F(u)+κμ in RN, u>0in RN, u(x)→0as |x|→∞, where F = F(t) grows up (at least) exponentially as t → ∞. Here N ≥ 2, κ > 0, and μ Lc1(RN) is nonnegative. Then, under a suitable integrability condition on μ, there exists a threshold parameter κ∗ > 0 such that problem (P) possesses a solution if 0 < κ < κ∗ and it does not possess no solutions if κ > κ∗. Furthermore, in the case of 2 ≤ N ≤ 9, problem (P) possesses a unique solution if κ = κ∗.

Original languageEnglish
Pages (from-to)968-992
Number of pages25
JournalAdvances in Nonlinear Analysis
Volume11
Issue number1
DOIs
Publication statusPublished - 2022 Jan 1

Keywords

  • exponential nonlinearity
  • inhomogeneous nonlinear elliptic equation

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