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Existence of positive solutions for a class of semipositone problem in whole ℝN

  • Claudianor O. Alves (a1), Angelo R. F. de Holanda (a1) and Jefferson A. dos Santos (a1)

Abstract

In this paper we show the existence of solution for the following class of semipositone problem P

$$\left\{\matrix{-\Delta u & = & h(x)(f(u)-a) & \hbox{in} & {\open R}^N, \cr u & \gt & 0 & \hbox{in} & {\open R}^N, \cr}\right.$$
where N ≥ 3, a > 0, h : ℝN → (0, + ∞) and f : [0, + ∞) → [0, + ∞) are continuous functions with f having a subcritical growth. The main tool used is the variational method together with estimates that involve the Riesz potential.

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