On positive solutions of nonlinear elliptic eigenvalue problems

Hendrik J. Kuiper

Research output: Contribution to journalArticle

34 Scopus citations

Abstract

Suppose Ω is a bounded region in Rn. In this paper we investigate the equation Lu=λF(x, u), u|∂Ω=0 where L is an elliptic partial differential operator and V 3 F(x, t) is a positive function on Ωx R1 which may have jump discontinuities with respect to t. We show that if certain conditions are satisfied there exists an unbounded continuum Λ of solutions (γ, u), with u(x)≥0, in the space R1×S. Here S is a Banach space of real valued functions such as(Formula presented.)

Original languageEnglish (US)
Pages (from-to)113-138
Number of pages26
JournalRendiconti del Circolo Matematico di Palermo
Volume20
Issue number2
DOIs
StatePublished - May 1971

ASJC Scopus subject areas

  • Mathematics(all)

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