Positive solutions of semilinear elliptic equations with small perturbations

Kajikiya, Ryuji

doi:10.1090/S0002-9939-2012-11569-2

Positive solutions of semilinear elliptic equations with small perturbations
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Proc. Amer. Math. Soc. 141 (2013), 1335-1342 Request permission

Abstract:

In this paper, we study the semilinear elliptic equation with a small perturbation. We assume the main term in the equation to have a mountain pass structure but do not suppose any condition for the perturbation term. Then we prove the existence of a positive solution. Moreover, we prove the existence of at least two positive solutions if the perturbation term is nonnegative.

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