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Existence of solutions for some fourth-order nonlinear elliptic problems. (English) Zbl 1179.35140

Authors’ abstract: We consider the existence of positive, negative and sign-changing solutions for some fourth order semilinear elliptic boundary value problems. We present new results on invariant sets of the gradient flows of the corresponding variational functionals. The structure of the invariant sets will be built into minimax procedures to construct the sign-changing solutions.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
35J61 Semilinear elliptic equations
35J35 Variational methods for higher-order elliptic equations
49J35 Existence of solutions for minimax problems
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