MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH

doi:10.1016/S0252-9602(18)30763-X

Abstract

Abstract:

In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,
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where Ω ⊂ R^N(N ≥ 3) is an open bounded domain with smooth boundary, 1< q < 2, λ > 0.2^*=2N/N-2 is the critical Sobolev exponent, f ∈L ^{2^*/(2^*-^q)} (Ω) is nonzero and nonnegative, and g ∈ C(Ω) is a positive function with k local maximum points. By the Nehari method and variational method, k +1 positive solutions are obtained. Our results complement and optimize the previous work by Lin[MR2870946, Nonlinear Anal. 75(2012) 2660-2671].

Key words: Semilinear elliptic equations, critical growth, positive solutions, Nehari method, variational method

Jiafeng LIAO, Yang PU, Chunlei TANG. MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH[J].Acta mathematica scientia,Series B, 2018, 38(2): 497-518.

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