Displaying similar documents to “Solvability of semilinear equations with strong nonlinearities and applications to elliptic boundary value problems”

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...

Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

In-Sook Kim, Jung-Hyun Bae (2013)

Open Mathematics

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Let X be an infinite-dimensional real reflexive Banach space such that X and its dual X* are locally uniformly convex. Suppose that T: X⊃D(T) → 2X* is a maximal monotone multi-valued operator and C: X⊃D(C) → X* is a generalized pseudomonotone quasibounded operator with L ⊂ D(C), where L is a dense subspace of X. Applying a recent degree theory of Kartsatos and Skrypnik, we establish the existence of an eigensolution to the nonlinear inclusion 0 ∈ T x + λ C x, with a regularization method...