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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 $f : X \to Y$ satisfies $\begin{matrix} f (x + i y) + f (x - i y) = 2 f (x) - 2 f (y) \end{matrix}$ for all $x$ , $y \in X$ , then the mapping $f : X \to Y$ satisfies $f (x + y) + f (x - y) = 2 f (x) + 2 f (y)$ for all $x$ , $y \in X$ . 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 Volterra integral equations in Henstock integrability setting.

Satco, Bianca-Renata (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Nonlocal conditions for lower semicontinuous parabolic inclusions.

Boucherif, Abdelkader (2011)

Advances in Difference Equations [electronic only]

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 $- Δ φ = M f (φ) / ({(\int_{Ω} f (φ))}^{p})$ , ${φ |}_{Ω} = 0$ 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-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.

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Non-linear eigenvalue problems and bifurcations for differentiable multivalued maps

Nonlinear Eigenvalue Problems with Monotonically Compact Operators. (Short Communication).

Nonlinear eigenvalue problems with monotonically compact operators.

Nonlinear ergodic theorems for a semitopological semigroup of non-Lipschitzian mappings without convexity.

Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space.

Nonlinear essential maps of Mönch, 1-set contractive demicopmact and monotone ${(S)}_{+}$ type.

Nonlinear Hammerstein equations and fixed points.

Nonlinear Mappings of Analytic Type in Banach Spaces.

Nonlinear mean ergodic theorems for semigroups in Hilbert spaces.

Nonlinear perturbations of quasi-linear delay control systems

Nonlinear Spectral Theories and Solvability of Nonlinear Hammerstein Equations