We prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991). Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.
A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem
SFECCI, ANDREA
2012-01-01
Abstract
We prove an existence result for radial solutions of a Neumann elliptic problem whose nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we introduce an alternative nonresonance condition with respect to the second eigenvalue which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991). Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical growth assumption.File in questo prodotto:
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