Asymptotic behaviour of positive solutions of semilinear elliptic problems with increasing powers

Lucio Boccardo,Liliane Maia,Benedetta Pellacci

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS（2022）

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摘要

We prove existence results of two solutions of the problem {L(u) + u(m-1) = lambda u(p-1) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where L(v) = -div(M(x)del v) is a linear operator, p is an element of (2, 2*] and lambda and m sufficiently large. Then their asymptotical limit as m -> +infinity is investigated showing different behaviours.

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关键词

Increasing powers in the lower order term, Asymptotical analysis, Semilinear elliptic equations

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