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Nonlinear Spectral Theories and Solvability of Nonlinear Hammerstein Equations

Halilović, Sanela (2010)

Mathematica Balkanica New Series

AMS Subj. Classification: 47J10, 47H30, 47H10We study some possibilities of nonlinear spectral theories for solving nonlinear operator equations. The main aim is to research a spectrum and establish some kind of nonlinear Fredholm alternative for Hammerstein operator KF.

Nonlinear stability of a quadratic functional equation with complex involution

Reza Saadati, Ghadir Sadeghi (2011)

Archivum Mathematicum

Let X , Y be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping f : X → Y satisfies f ( x + i y ) + f ( x - i y ) = 2 f ( x ) - 2 f ( y ) for all x , y ∈ X , then the mapping f : X → Y satisfies f ( x + y ) + f ( x - y ) = 2 f ( x ) + 2 f ( y ) for all x , y ∈ X . Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method.

Nonlinear Variational Inequalities Depending on a Parameter

Goeleven, D., Théra, M. (1995)

Serdica Mathematical Journal

This paper develops the results announced in the Note [14]. Using an eigenvalue problem governed by a variational inequality, we try to unify the theory concerning the post-critical equilibrium state of a thin elastic plate subjected to unilateral conditions.

Nonlocal elliptic problems

Andrzej Krzywicki, Tadeusz Nadzieja (2000)

Banach Center Publications

Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem - Δ φ = M f ( φ ) / ( ( ∫ Ω f ( φ ) ) p ) , φ | Ω = 0 are given.

Nonlocal systems of BVPs with asymptotically superlinear boundary conditions

Christopher S. Goodrich (2012)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions, and we examine conditions under which such problems will have at least one positive solution. By imposing only an asymptotic growth condition on the nonlinear boundary functions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be realized as Lebesgue-Stieltjes integrals possessing signed Borel...

Non-monotoneous parallel iteration for solving convex feasibility problems

Gilbert Crombez (2003)

Kybernetika

The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in an Euclidean space, sometimes leads to slow convergence of the constructed sequence. Such slow convergence depends both on the choice of the starting point and on the monotoneous behaviour of the usual algorithms. As there is normally no indication of how to choose the starting point in order to avoid slow convergence, we present in this paper a non-monotoneous parallel algorithm...

Non-self mappings in modular spaces and common fixed point theorems

Abdolrahman Razani, Valdimir Rakočević, Zahraa Goodarzi (2010)

Open Mathematics

The aim of this paper, is to introduce the convex structure (specially, Takahashi convex structure) on modular spaces. Moreover, we are interested in proving some common fixed point theorems for non-self mappings in modular space.

Nonzero and positive solutions of a superlinear elliptic system

Mario Zuluaga Uribe (2001)

Archivum Mathematicum

In this paper we consider the existence of nonzero solutions of an undecoupling elliptic system with zero Dirichlet condition. We use Leray-Schauder Degree Theory and arguments of Measure Theory. We will show the existence of positive solutions and we give applications to biharmonic equations and the scalar case.

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