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Multiple critical points for a class of nonlinear functionals. (English) Zbl 1230.58014
The authors prove a multiplicity result concerning the critical points of a class of functionals involving local and nonlocal nonlinearities. The result is applied to the nonlinear Schrödinger-Maxwell system in $\Bbb R^{3}$ and to the nonlinear elliptic Kirchhoff equation in $\Bbb R^{N}$ assuming on the local nonlinearity the general hypotheses introduced by Berestycki and Lions.

MSC:
58E50Applications of variational methods in infinite-dimensional spaces
58E05Abstract critical point theory
35J20Second order elliptic equations, variational methods
35J60Nonlinear elliptic equations
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References:
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