On the spectrum of a nonlinear operator
On the spectrum of the -biharmonic operator.
On the splitting methods and the proximal point algorithm for maximal monotone operators.
On the Stability of Jungck–Mann, Jungck–Krasnoselskij and Jungck Iteration Processes in Arbitrary Banach Spaces
In this paper, we establish some stability results for the Jungck–Mann, Jungck–Krasnoselskij and Jungck iteration processes in arbitrary Banach spaces. These results are proved for a pair of nonselfmappings using the Jungck–Mann, Jungck–Krasnoselskij and Jungck iterations. Our results are generalizations and extensions to a multitude of stability results in literature including those of Imoru and Olatinwo [8], Jungck [10], Berinde [1] and many others.
On the stability of some fixed point iteration procedures with errors.
On the Stability of the Ritz Procedure for Nonlinear Problems.
On the structure of the set of solutions of a functional equation with applications to boundary value problems
On the théorème fondamental of J. Leray and J. Schauder
On the topological dimension of the solutions sets for some classes of operator and differential inclusions
In the present paper, we give the lower estimation for the topological dimension of the fixed points set of a condensing continuous multimap in a Banach space. The abstract result is applied to the fixed point set of the multioperator of the form where is the superposition multioperator generated by the Carathéodory type multifunction F and S is the shift of a linear injective operator. We present sufficient conditions under which this set has the infinite topological dimension. In the last...
On the unique constructive solvability of Hammerstein equations.
On the unique solvability of a nonlocal phase separation problem for multicomponent systems
A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction potential...
On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation
We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient.
On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients
We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution....
On Threshold Eigenvalues and Resonances for the Linearized NLS Equation
We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.
On two problems studied by A. Ambrosetti
We study the Ambrosetti–Prodi and Ambrosetti–Rabinowitz problems.We prove for the first one the existence of a continuum of solutions with shape of a reflected (-shape). Next, we show that there is a relationship between these two problems.
On variational impulsive boundary value problems
Using the variational approach, we investigate the existence of solutions and their dependence on functional parameters for classical solutions to the second order impulsive boundary value Dirichlet problems with L1 right hand side.
One-parameter global bifurcation in a multiparameter problem
Open problems for nonlinear dominated operators on locally bounded spaces of measurable functions.
Operadores Integrales De Hammerstein, Su Espectro Y Aplicaciones.
Operator-splitting methods for general mixed variational inequalities.