Multiple solutions of a sublinear Schrödinger equation

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17 Citations (Scopus)

Abstract

In this paper we study the Schrödinger equation of the form (P λ) -Δu + a(x)u = λb(x) f (u), x ⊂ ℝN, u ⊂ H1 (ℝN), where λ > 0 is a parameter, a and b are positive potentials, while the nonlinear term f : ℝ → ℝ is sublinear at infinity. Two cases will be considered: (i) f is superlinear at the origin; (ii) f does not satisfy any asymptotical property at the origin. In both situations, the existence of certain multiple weak solutions of (Pλ) are established for some λ > 0.

Original languageEnglish
Pages (from-to)291-301
Number of pages11
JournalNonlinear Differential Equations and Applications
Volume14
Issue number3-4
DOIs
Publication statusPublished - Nov 2007

Keywords

  • Multiple solutions
  • Nonlinear Schrödinger equations
  • Sublinearity at infinity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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