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Symmetry and multiple solutions for certain quasilinear elliptic equations. (English) Zbl 1326.35144

The authors establish existence and multiplicity of symmetric solutions for abstract eigenvalue problems \[ J'(u) = \lambda {\mathcal F}'(u) \] where \(J\) is a convex \(C^1\) functional and \[ {\mathcal F}(u) = \int_\Omega F(x,u(x))\;dx, \;\;\;\;F(x,t) = \int_0^t f(x,s) \;ds. \] Connections with existing results and concrete examples are given.

MSC:

35J62 Quasilinear elliptic equations
35A15 Variational methods applied to PDEs
35J15 Second-order elliptic equations
35J20 Variational methods for second-order elliptic equations
35B06 Symmetries, invariants, etc. in context of PDEs
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Full Text: Euclid