Fixed points of cone compression and expansion multimaps defined on Fréchet spaces: the projective limit approach.
General ways of constructing accelerating Newton-like iterations on partially ordered topological spaces.
Generalized communication conditions and the eigenvalue problem for a monotone and homogenous function
This work is concerned with the eigenvalue problem for a monotone and homogenous self-mapping of a finite dimensional positive cone. Paralleling the classical analysis of the (linear) Perron–Frobenius theorem, a verifiable communication condition is formulated in terms of the successive compositions of , and under such a condition it is shown that the upper eigenspaces of are bounded in the projective sense, a property that yields the existence of a nonlinear eigenvalue as well as the projective...
Generalized variational-like inequalities for pseudo-monotone type III operators
Our aim in this paper is mainly to prove some existence results for solutions of generalized variational-like inequalities with (η,h)-pseudo-monotone type III operators defined on non-compact sets in topological vector spaces.
Global asymptotic stability of inhomogeneous iterates.
Hybrid fixed point theory for right monotone increasing multi-valued mappings and neutral functional differential inclusions
In this paper, some hybrid fixed point theorems for the right monotone increasing multi-valued mappings in ordered Banach spaces are proved via measure of noncompactness and they are further applied to the neutral functional nonconvex differential inclusions involving discontinuous multi-functions for proving the existence results under mixed Lipschitz, compactness and right monotonicity conditions. Our results improve the multi-valued hybrid fixed point theorems of Dhage (Dhage, B. C., A fixed...
Impulsive integral equations in Banach spaces and applications.
Inversion in some algebras of singular integral operators.
Iterations of concave maps, the Perron-Frobenius theory, and applications to circle packings.
Iterative Einschliessungen von Lösungen nichtlinearer Differentialgleichungen durch Newton-ähnliche Iterationsverfahren
In der vorliegenden Arbeit untersuchen wir monoton einschliessende Newton-ähnliche Iterationsverfahren zur näherungsweisen Lösung verschiedener Klassen vonnichtlinearen Differentialgleichungen. Die behandelten Methoden sind auch für nichtkonvexe Nichtlinearitäten anwendbar. Ferner konstruieren wir einschliessende Startnäherungen für diese Verfahren, so dass wir die Existenz der Lösungen der gegebenen Differentialgleichungen sichern können. Die Konvergenz der Verfahren wird auch für den Fall bewiesen,...
Monotone iterative technique and connectedness of the set of solutions
The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described.
Multiple fixed points of positive mappings.
Multiple positive solutions of a singular fractional boundary value problem.
Multiplicity results for sign-changing solutions of an operator equation in ordered Banach space
In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions.
Nonlinear impulsive Volterra integral equations in Banach spaces and applications.
Nonlinear Mappings of Analytic Type in Banach Spaces.
Nonlocal systems of BVPs with asymptotically superlinear boundary conditions
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...
N-th order impulsive integro-differential equations in Banach spaces.
On discontinuous implicit differential equations in ordered Banach spaces with discontinuous implicit boundary conditions
We consider the existence of extremal solutions to second order discontinuous implicit ordinary differential equations with discontinuous implicit boundary conditions in ordered Banach spaces. We also study the dependence of these solutions on the data, and cases when the extremal solutions are obtained as limits of successive approximations. Examples are given to demonstrate the applicability of the method developed in this paper.
On existence of extremal solutions of nonlinear functional integral equations in Banach algebras.