Nonlinear analysis. New arguments and results.
Si presentano condizioni sufficienti in forma astratta per l'esistenza di soluzioni di equazioni operazionali non lineari la cui parte lineare non è autoaggiunta.
Si presentano condizioni sufficienti in forma astratta per l'esistenza di soluzioni di equazioni operazionali non lineari la cui parte lineare non è autoaggiunta.
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.
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 . In this problem the maximal monotone term is required to be defined everywhere in the state space . The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form . In this case the maximal...
We establish five theorems giving lists of nonlinear contractive conditions which turn out to be mutually equivalent. We derive them from some general lemmas concerning subsets of the plane which may be applied both in the single- or set-valued case as well as for a family of mappings. A separation theorem for concave functions is proved as an auxiliary result. Also, we discuss briefly the following problems for several classes of contractions: stability of procedure of successive approximations,...
This paper considers the initial-boundary value problem for the nonlinear diffusion equation with the perturbation term in an unbounded domain with smooth bounded boundary, where , , , is a single-valued maximal monotone function on , e.g., and is a function on which can be regarded as a Lipschitz continuous operator from to . The present work establishes existence and estimates for the above problem.
In this paper existence and multiplicity of solutions of the elliptic problem in on , are discussed provided the parameters and are close to the first eigenvalue . The sufficient conditions...