Name: On the Existence of Positive Solutions of Semilinear Elliptic Equations
Creator: Lions, Pierre-Louis
Keywords: Bifurcations in context of PDEs, positive solutions, bifurcation diagrams, Nonlinear boundary value problems for linear elliptic equations, semilinear elliptic equations, 0101 mathematics, Degree, winding number, 01 natural sciences

On the existence of positive solutions of semilinear elliptic equations

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 1982 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Review, volume 24, pages 441-467 (issn: 0036-1445, eissn: 1095-7200,

Authors: Lions, Pierre-Louis;

doi: 10.1137/1024101

On the Existence of Positive Solutions of Semilinear Elliptic Equations

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Abstract

In this paper we study the existence of positive solutions of semilinear elliptic equations. Various possible behaviors of nonlinearity are considered, and in each case nearly optimal multiplicity results are obtained. The results are also interpreted in terms of bifurcation diagrams.

Keywords

Bifurcations in context of PDEs, positive solutions, bifurcation diagrams, Nonlinear boundary value problems for linear elliptic equations, semilinear elliptic equations, Degree, winding number

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