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The numbers of positive solutions by the Lusternik-Schnirelmann category for a quasilinear elliptic system critical with Hardy terms. (English) Zbl 1475.35148

Summary: In this paper, we study the quasilinear elliptic system with Sobolev critical exponent involving both concave-convex and Hardy terms in bounded domains. By employing the technique introduced by V. Benci and G. Cerami [Arch. Ration. Mech. Anal. 114, No. 1, 79–93 (1991; Zbl 0727.35055)], we obtain at least \(\operatorname{cat}(\Omega) + 1\) distinct positive solutions.

MSC:

35J57 Boundary value problems for second-order elliptic systems
35B09 Positive solutions to PDEs
35B33 Critical exponents in context of PDEs
35J62 Quasilinear elliptic equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian

Citations:

Zbl 0727.35055
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References:

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