Infinite multiplicity for inhomogeneous supercritical problem in entire space

Details Infinite multiplicity for inhomogeneous supercritical problem in entire space Infinite multiplicity for inhomogeneous supercritical problem in entire space

2010-01-12

arxiv.org/abs/1001.1787v1

Mathematics

Analysis of PDEs

10 pages

Scientific paper

In this paper, we will prove the existence of infinitely many positive
solutions to the following supercritical problem by using the Liapunov-Schmidt
reduction method and asymptotic analysis:
{ll}\Delta u + u^{p}+f(x)=0, u>0 {in} R^{n},
\lim_{|x|\to\infty}u(x)\to 0.

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