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Doubly resonant semilinear elliptic problems via nonsmooth critical point theory. (English) Zbl 1187.35083
Summary: We consider the existence of weak solutions for classical doubly resonant semilinear elliptic problems. We show how the main technical assumptions can be used to define appropriate metrics on the underlying function space, so that extensions of the results already known in the literature can be obtained using only basic facts from critical point theory for continuous functionals on complete metric spaces.
35J61Semilinear elliptic equations
58E05Abstract critical point theory
35J25Second order elliptic equations, boundary value problems
35J91Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35J20Second order elliptic equations, variational methods
35B38Critical points in solutions of PDE
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