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 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...

* Correspondence: jinliang@sjtu. edu.cn Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China Full list of author information is available at the end of the article Abstract We are concerned with the existence of mild solutions to the Cauchy problem for fractional evolution equations of neutral type with almost sectorial operators dq dtq (x(t) − h(t, x(t))) = −A...

For an R-bounded families of operators on L1 we associate a family of representing measures and show that they form a weakly compact set. We consider a sectorial operator A which generates an R-bounded semigroup on L1. We show that given 2 > 0 there is an invertible operator U : L1 → L1 with ‖U − I‖ < 2 such that for some positive Borel function w we have U(D(A)) ⊃ L1(w).

If z 7→ az is a holomorphic function with values in the sectorial forms in a Hilbert space, then the associated operator valued function z 7→ Az is resolvent holomorphic. We give a proof of this result of Kato, on the basis of the Lax-Milgram lemma. We also show that the C0-semigroups Tz generated by −Az depend holomorphically on z. MSC 2010: 47A07, 47B44, 47D06

1 This is one of three background papers commissioned by the United Nations Forum for Forests. Background paper 1: Focuses on economic contributions of forests, by Agrawal, Shepherd and Cashore; Background Paper 2: Forests and cross-sectorial linkages, by Lele, Karsenty, Benson, Fétiveau, Agarwal and Goswami; and Background paper 3: The role of forests in a future world, by Agrawal et al. This ...

Dafermos regularization is a viscous regularization of hyperbolic conservation laws that preserves solutions of the form u = û(X/T ). A RiemannDafermos solution is a solution of the Dafermos regularization that is close to a Riemann solution of the conservation law. Using self-similar coordinate x = X/T , Riemann-Dafermos solutions become stationary. In a suitable Banach space, we show that the...