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Multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent. (English) Zbl 1192.35064

Summary: We study the decomposition of the Nehari manifold via the combination of concave and convex nonlinearities. Furthermore, we use this result and the Ljusternik-Schnirelmann category to prove the existence of multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent.

MSC:

35J61 Semilinear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J20 Variational methods for second-order elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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