Evolution inclusions of the subdifferential type depending on a parameter.
Evolution inclusions of the subdifferential type depending on a parameter
In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set is both Vietoris and Hausdorff metric continuous in . Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.
Evolution problems associated with nonconvex closed moving sets with bounded variation.
Existence and asymptotic behaviour of solutions of a nonlinear evolution problem
We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for where is the pseudo-Laplacian operator.
Existence and density results for retarded subdifferential evolution inclusions
In this paper we study Cauchy problems for retarded evolution inclusions, where the Fréchet subdifferential of a function F:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone subdifferential of oder two is present. First we establish the existence of extremal trajectories and we show that the set of these trajectories is dense in the solution set of the original convex problem for the norm topology of the Banach space C([-r, T₀], Ω) ("strong relaxation theorem")....
Existence and global asymptotical stability of periodic solution for the -periodic logistic system with time-varying generating operators and -periodic impulsive perturbations on Banach spaces.
Existence and limiting behaviour for damped nonlinear evolution equations with nonlocal terms
Existence and relaxation results for nonlinear evolution inclusions revisited.
Existence and relaxation results for nonlinear second order evolution inclusions
In this paper we study nonlinear evolution inclusions associated with second order equations defined on an evolution triple. We prove two existence theorems for the cases where the orientor field is convex valued and nonconvex valued, respectively. We show that when the orientor field is Lipschitzean, then the set of solutions of the nonconvex problem is dense in the set of solutions of the convexified problem.
Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem.
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.