Abstract
In this paper we show the existence and multiplicity of positive solutions using the sub-supersolution method and Mountain Pass Theorem in a general singular system which the operator is not homogeneous neither linear.
Highlights
In this paper we treat the question of the existence and multiplicity of positive solutions for the following class of singular systems of nonlinear elliptic equation h1(x)u−γ1
In order to prove (ii), we invoke Lemma 2.1 and maximum principle once again to claim that there exists an unique positive solution 0 < u ∈ W01,q1 (Ω) satisfying
In our result we prove that the functional Φ satisfies the two geometries of the Mountain Pass Theorem [1]
Summary
We assume the conditions below to prove the existence of two solutions for problem (1.1). By considering the hypothesis (A2), we argument as [8, Lemma 2.4] to obtain the following inequality From Lemma 2.1 and maximum principle, there exists an unique positive solution 0 < u ∈ W01,q1 (Ω) satisfying the problem below
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