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On the multiplicity of solutions for a fully nonlinear Emden-Fowler equation. (English) Zbl 1057.35007

Summary: We are concerned with the existence of two solutions for a fully nonlinear Emden-Fowler type equation. One solution is obtained via local minimization while the second solution follows by a mountain pass argument. A non-existence result in strictly star-shaped domains is also proven.

MSC:

35D05 Existence of generalized solutions of PDE (MSC2000)
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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