Solution curves for semilinear equations on a ball

1997/01/01 by Philip Korman · 4 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.1090/s0002-9939-97-04119-1

Abstract

We show that the set of positive solutions of semilinear Dirichlet problem on a ball of radius R in Rⁿ Δ u+λ f(u)=0 \text for |x|<R, u=0 \text on |x|=R consists of smooth curves. Our results can be applied to compute the direction of bifurcation. We also give an easy proof of a uniqueness theorem due to Smoller and Wasserman (1984).

Cited by

• A limit equation and bifurcation diagrams of semilinear elliptic equations with general supercritical growth
• Singular extremal solutions for supercritical elliptic equations in a ball
• A bifurcation diagram of solutions to semilinear elliptic equations with general supercritical growth
• Structure of the solution set of a regularized MEMS model

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• Bifurcation diagrams for semilinear elliptic equations with singular weights in two dimensions