An abstract version of the resonance theorem
An algorithm based on resolvent operators for solving positively semidefinite variational inequalities. (An algorithm based on resolvant operators for solving positively semidefinite variational inequalities.)
An algorithm for finding a common solution for a system of mixed equilibrium problem, quasivariational inclusion problem, and fixed point problem of nonexpansive semigroup.
An application of hybrid steepest descent methods for equilibrium problems and strict pseudocontractions in Hilbert spaces.
An approximation method for continuous pseudocontractive mappings.
An approximation of solutions of variational inequalities.
An eigenvalue problem for elliptic systems.
An elliptic equation with no monotonicity condition on the nonlinearity
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree...
An Elliptic Neumann Problem with Subcritical Nonlinearity
We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.
An Error Analysis for the Secant Method.
An existence and uniqueness result for semilinear equations with Lipschitz nonlinearity.
An existence theorem for the Urysohn integral equation in Banach spaces
An extension of a multiplicity theorem by Ricceri with an application to a class of quasilinear equations
A recent multiplicity result by Ricceri, stated for equations in Hilbert spaces, is extended to a wider class of Banach spaces. Applications to nonlinear boundary value problems involving the p-Laplacian are presented.
An extension of invertibility of Hammerstein-type operators
My aim is to show that some properties, proved to be true for the square matrices, are true for some not necessarily linear operators on a linear space, in particular, for Hammerstein-type operators.
An extension of the auxiliary problem principle to nonsymmetric auxiliary operators
An Extension of the Auxiliary Problem Principle to Nonsymmetric Auxiliary Operators
To find a zero of a maximal monotone operator, an extension of the Auxiliary Problem Principle to nonsymmetric auxiliary operators is proposed. The main convergence result supposes a relationship between the main operator and the nonsymmetric component of the auxiliary operator. When applied to the particular case of convex-concave functions, this result implies the convergence of the parallel version of the Arrow-Hurwicz algorithm under the assumptions of Lipschitz and partial Dunn properties...
An extension of the topological degree in Hilbert space.
An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings.
An extragradient approximation method for variational inequality problem on fixed point problem of nonexpensive mappings and monotone mappings
We introduce an iterative sequence for finding the common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for tree inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply to finding solutions of a general system of variational inequality and a zero of a maximal monotone...
An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems
In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.