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Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities. (English) Zbl 1129.35372

Summary: Using variational arguments, we prove some nonexistence and multiplicity results for positive solutions of a system of \(p\)-Laplace equations of gradient form. Then we study a \(p\)-Laplace-type problem with nonlinear boundary conditions.

MSC:

35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35J50 Variational methods for elliptic systems
35J65 Nonlinear boundary value problems for linear elliptic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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