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Neumann boundary value problems across resonance

Ginés López, Juan-Aurelio Montero-Sánchez (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We obtain an existence-uniqueness result for a second order Neumann boundary value problem including cases where the nonlinearity possibly crosses several points of resonance. Optimal and Schauder fixed points methods are used to prove this kind of results.

Nonlinear analysis. New arguments and results.

Lamberto Cesari (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si presentano condizioni sufficienti in forma astratta per l'esistenza di soluzioni di equazioni operazionali non lineari la cui parte lineare non è autoaggiunta.

Nonlinear analysis. New arguments and results. II.

Lamberto Cesari (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We continue here the discussion in part I, and we state and prove further sufficient conditions for the existence of a solution to nonselfadjoint problems.

Nonlinear boundary value problems for second order differential inclusions

Sophia Th. Kyritsi, Nikolaos M. Matzakos, Nikolaos S. Papageorgiou (2005)

Czechoslovak Mathematical Journal

In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator of the form x a ( x , x ' ) ' . In this problem the maximal monotone term is required to be defined everywhere in the state space N . The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ( a ( x ) x ' ) ' . In this case the maximal...

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