The existence of one non-trivial solution for a nonlinear problem on compact d-dimensional () Riemannian manifolds without boundary, is established. More precisely, a recent critical point result for differentiable functionals is exploited, in order to prove the existence of a determined open interval of positive eigenvalues for which the considered problem admits at least one non-trivial weak solution. Moreover, as a consequence of our approach, a multiplicity result is presented, requiring the validity of the Ambrosetti-Rabinowitz hypothesis. Successively, the Cerami compactness condition is studied in order to obtain a similar multiplicity theorem in superlinear cases. Finally, applications to Emden-Fowler type equations are presented.

Nonlinear elliptic problems on Riemannian manifolds and applications to Emden-Fowler type equations

Molica Bisci G;
2013-01-01

Abstract

The existence of one non-trivial solution for a nonlinear problem on compact d-dimensional () Riemannian manifolds without boundary, is established. More precisely, a recent critical point result for differentiable functionals is exploited, in order to prove the existence of a determined open interval of positive eigenvalues for which the considered problem admits at least one non-trivial weak solution. Moreover, as a consequence of our approach, a multiplicity result is presented, requiring the validity of the Ambrosetti-Rabinowitz hypothesis. Successively, the Cerami compactness condition is studied in order to obtain a similar multiplicity theorem in superlinear cases. Finally, applications to Emden-Fowler type equations are presented.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11576/2664258
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