A strong convergence theorem for a common fixed point of two sequences of strictly pseudocontractive mappings in Hilbert spaces and applications.
A strong convergence theorem for a family of quasi--nonexpansive mappings in a Banach space.
A study of variational inequalities for set-valued mappings.
A superquadratic method for solving variational inclusions under weak conditions.
A system of generalized mixed equilibrium problems and fixed point problems for pseudocontractive mappings in Hilbert spaces.
A system of nonlinear operator equations for a mixed family of fuzzy and crisp operators in probabilistic normed spaces.
A topological structure of solution sets to evolution systems
A topological version of the Ambrosetti-Prodi theorem
The existence of at least two solutions for nonlinear equations close to semilinear equations at resonance is obtained by the degree theory methods. The same equations have no solutions if one slightly changes the right-hand side. The abstract result is applied to boundary value problems with specific nonlinearities.
A two-dimensional Hammerstein problem: The linear case.
A Unified Approach for Constructing Fast Two-Step Newton-like Methods.
A unifying convergence analysis of Newton's method for twice Fréchet-differentiable operators
We provide a local as well as a semilocal convergence analysis for Newton's method using unifying hypotheses on twice Fréchet-differentiable operators in a Banach space setting. Our approach extends the applicability of Newton's method. Numerical examples are also provided.
A unifying semilocal convergence theorem for Newton-like methods in Banach space.
A unifying theorem on Newton's method in a Banach space with a convergence structure under weak assumptions.
A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions
We consider a simple reaction-diffusion system exhibiting Turing's diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential...
A variational approach to bifurcation points of a reaction-diffusion system with obstacles and Neumann boundary conditions
Given a reaction-diffusion system which exhibits Turing's diffusion-driven instability, the influence of unilateral obstacles of opposite sign (source and sink) on bifurcation and critical points is studied. In particular, in some cases it is shown that spatially nonhomogeneous stationary solutions (spatial patterns) bifurcate from a basic spatially homogeneous steady state for an arbitrarily small ratio of diffusions of inhibitor and activator, while a sufficiently large ratio is necessary in the...
A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary
A Viscoelastic Frictionless Contact Problem with Adhesion
We consider a mathematical model which describes the equilibrium between a viscoelastic body in frictionless contact with an obstacle. The contact is modelled with normal compliance, associated with Signorini's conditions and adhesion. The adhesion is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution....
A viscosity approximation method for finding common solutions of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces.
A viscosity hybrid steepest descent method for generalized mixed equilibrium problems and variational inequalities for relaxed cocoercive mapping in Hilbert spaces.
A viscosity of Cesàro mean approximation methods for a mixed equilibrium, variational inequalities, and fixed point problems.