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Multiplicity results for sign-changing solutions of an operator equation in ordered Banach space

Xian Xu, Bingjin Wang (2009)

Mathematica Bohemica

In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions.

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.

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