We study regularizing properties for transition semigroups related to Ornstein Uhlenbeck processes with values in a Banach space E which is continuously and densely embedded in a real and separable Hilbert space H . Namely we study conditions under which the transition semigroup maps continuous and bounded functions into differentiable functions. Via a Girsanov type theorem such properties exte...

where Ω ⊂ R is a bounded smooth domain, f : Ω × R ® R and M : R ® R are continuous functions. The existence and multiplicity results for Equation (1) are considered in [1-3] by using variational methods and fixed point theorems in cones of ordered Banach space with space dimension is one. On the other hand, The four-order semilinear elliptic problem { 2u + c u = f (x, u), in , u = u = 0, on ∂ ,...

The Banach contraction principle is used to investigate the existence and uniqueness of solutions for first and second order impulsive semilinear neutral functional differential equations in Banach spaces. 2000 Mathematics Subject Classification: 34A37, 34G20, 34K25.

We study almost automorphic (mild) solutions of the semilinear fractional equation ∂ t u = Au + ∂ α−1 t f(·, u), 1 < α < 2, considered in a Banach space X, where A is a linear operator of sectorial type ω < 0. We prove the existence and uniqueness of an almost automorphic mild solution assuming f(t, x) is almost automorphic in t for each x ∈ X, satisfies some Lipschitz type conditions and takes...

We propose and study a numerical method for time discretization of linear and semilinear integro-partial differential equations that are intermediate between diffusion and wave equations, or are subdiffusive. The method uses convolution quadrature based on the second-order backward differentiation formula. Second-order error bounds of the time discretization and regularity estimates for the sol...

In this paper, we study the existence of weighted pseudo almost automorphic mild solutions of integro-differential equations with fractional order 1 < α < 2, here A is a linear densely defined operator of sectorial type on a complex Banach space X. This paper also deals with existence of weighted pseudo almost automorphic mild solutions of semilinear integro-differential eqautions with A is the...

We consider the existence and uniqueness of Weighted Pseudo almost automorphic solutions to the non-autonomous semilinear differential equation in a Banach space X : ( ) = ( ) ( ) ( , ( )), ' u t A t u t f t u t t R where ( ), , A t t R generates an exponentially stable evolution family { ( , )} U t s and : f X X R satisfies a Lipschitz condition with respect to the second argument. MSC 2010: 4...