Existence of solutions for discontinuous functional equations and elliptic boundary-value problems.
Existence of solutions for discontinuous hyperbolic partial differential equations in Banach algebras.
Existence of solutions for elliptic equations having natural growth terms in Orlicz spaces.
Existence of solutions for elliptic systems involving operators in divergence form.
Existence of solutions for elliptic systems with critical Sobolev exponent.
Existence of solutions for elliptic systems with nonlocal terms in one dimension.
Existence of solutions for evolution equations in Hilbert spaces with anti-periodic boundary conditions and its applications
We establish the existence of solutions for evolution equations in Hilbert spaces with anti-periodic boundary conditions. The energies associated to these evolution equations are quadratic forms. Our approach is based on application of the Schaefer fixed-point theorem combined with the continuity method.
Existence of solutions for fourth-order PDEs with variable exponents.
Existence of solutions for hyperbolic system of second order outside a domain.
Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces
We study the existence of mild solutions for a class of impulsive fractional partial neutral integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the fixed point theorem for discontinuous multi-valued operators due to Dhage and properties of the α-resolvent operator. An example is given to illustrate the...
Existence of solutions for infinite systems of parabolic equations with functional dependence
The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method.
Existence of solutions for Navier problems with degenerate nonlinear elliptic equations
In this paper we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations in the setting of the weighted Sobolev spaces.
Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions
The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet -Laplace operator.
Existence of solutions for nonlinear parabolic problems
We consider nonlinear parabolic boundary value problems. First we assume that the right hand side term is discontinuous and nonmonotone and in order to have an existence theory we pass to a multivalued version by filling in the gaps at the discontinuity points. Assuming the existence of an upper solution and of a lower solution such that , and using the theory of nonlinear operators of monotone type, we show that there exists a solution and that the set of all such solutions is compact in...
Existence of solutions for nonlinear parabolic systems via weak convergence of truncations.
Existence of solutions for non-linear systems of differential-functional equations of parabolic type in an arbitrary domain
Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators.
Existence of solutions for one-dimensional wave equations with nonlocal conditions.
Existence of solutions for -Laplacian equations.
Existence of solutions for quasilinear degenerate elliptic equations.