Existence and uniqueness of solutions for a class of infinite-horizon systems derived from optimal control.
Existence and uniqueness of solutions for fourth-order boundary-value problems in Banach spaces.
Existence and uniqueness of solutions for nonlinear alternative problems in a Banach space
Existence and uniqueness of solutions to a semilinear functional-differential evolution nonlocal Cauchy problem.
Existence and uniqueness theorem for a solution of fuzzy differential equations.
Existence for implicit differential equations in Banach spaces
We prove two existence results on abstract differential equations of the type and we give some applications of them to partial differential equations.
Existence of approximate solution to abstract nonlocal Cauchy problem.
Existence of extremal periodic solutions for nonlinear evolution inclusions
We consider a nonlinear evolution inclusion defined in the abstract framework of an evolution triple of spaces and we look for extremal periodic solutions. The nonlinear operator is only pseudomonotone coercive. Our approach is based on techniques of multivalued analysis and on the theory of operators of monotone-type. An example of a parabolic distributed parameter system is also presented.
Existence of mild solutions for fractional evolution equations with nonlocal initial conditions
This paper discusses the existence of mild solutions for a class of semilinear fractional evolution equations with nonlocal initial conditions in an arbitrary Banach space. We assume that the linear part generates an equicontinuous semigroup, and the nonlinear part satisfies noncompactness measure conditions and appropriate growth conditions. An example to illustrate the applications of the abstract result is also given.
Existence of mild solutions for quasilinear integrodifferential equations with impulsive conditions.
Existence of mild solutions for semilinear equation of evolution
The aim of this paper is to give an existence theorem for a semilinear equation of evolution in the case when the generator of semigroup of operators depends on time parameter. The paper is a generalization of [2]. Basing on the notion of a measure of noncompactness in Banach space, we prove the existence of mild solutions of the equation considered. Additionally, the applicability of the results obtained to control theory is also shown. The main theorem of the paper allows to characterize the set...
Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces
In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.
Existence of mild solutions on semiinfinite interval for first order differential equation with nonlocal condition
In this paper we investigate the existence of mild solutions defined on a semiinfinite interval for initial value problems for a differential equation with a nonlocal condition. The results is based on the Schauder-Tychonoff fixed point theorem and rely on a priori bounds on solutions.
Existence of periodic solutions for a class of nonlinear evolution equations.
Existence of pseudo-almost automorphic mild solutions to some nonautonomous partial evolution equations.
Existence of -almost periodic solutions to a class of nonautonomous stochastic evolution equations.
Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space
In this paper we deal with the boundary value problem in the Hilbert space. Existence of a solutions is proved by using the method of lower and upper solutions. It is not necessary to suppose that the homogeneous problem has only the trivial solution. We use some results from functional analysis, especially the fixed-point theorem in the Banach space with a cone (Theorem 4.1, [5]).
Existence of solutions and controllability of nonlinear integro-differential systems in Banach spaces.
Existence of solutions for hyperbolic differential inclusions in Banach spaces
In this paper we examine nonlinear hyperbolic inclusions in Banach spaces. With the aid of a compactness condition involving the ball measure of noncompactness we prove two existence theorems. The first for problems with convex valued orientor fields and the second for problems with nonconvex valued ones.
Existence of solutions for integrodifferential inclusions in Banach spaces
In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.