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.

Nonlinear elliptic differential equations with multivalued nonlinearities

Antonella Fiacca, Nikolaos M. Matzakos, Nikolaos S. Papageorgiou, Raffaella Servadei (2003)

Czechoslovak Mathematical Journal

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In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ . Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed...

Existence of solutions of perturbed O.D.E.'s in Banach spaces

Giovanni Emmanuele (1991)

Commentationes Mathematicae Universitatis Carolinae

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We consider a perturbed Cauchy problem like the following (PCP) x ' = A ( t , x ) + B ( t , x ) x ( 0 ) = x 0 and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).