Displaying similar documents to “Equations with discontinuous nonlinear semimonotone operators”

Surjectivity results for nonlinear mappings without oddness conditions

W. Feng, Jeffrey Ronald Leslie Webb (1997)

Commentationes Mathematicae Universitatis Carolinae

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Surjectivity results of Fredholm alternative type are obtained for nonlinear operator equations of the form λ T ( x ) - S ( x ) = f , where T is invertible, and T , S satisfy various types of homogeneity conditions. We are able to answer some questions left open by Fuč’ık, Nečas, Souček, and Souček. We employ the concept of an a -stably-solvable operator, related to nonlinear spectral theory methodology. Applications are given to a nonlinear Sturm-Liouville problem and a three point boundary value problem recently...

The Neumann problem for quasilinear differential equations

Tiziana Cardinali, Nikolaos S. Papageorgiou, Raffaella Servadei (2004)

Archivum Mathematicum

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In this note we prove the existence of extremal solutions of the quasilinear Neumann problem - ( | x ' ( t ) | p - 2 x ' ( t ) ) ' = f ( t , x ( t ) , x ' ( t ) ) , a.e. on T , x ' ( 0 ) = x ' ( b ) = 0 , 2 ≤ p < ∞ in the order interval [ ψ , ϕ ] , where ψ and ϕ are respectively a lower and an upper solution of the Neumann problem.