This paper is concerned with the study of weighted pseudo almost periodic mild solutions for semilinear boundary differential equations. Namely, some sufficient conditions for the existence and uniqueness of weighted pseudo almost periodic mild solutions of semilinear boundary differential equations are obtain.

We consider a Cauchy problem for a fractional semilinear differential inclusions involving Caputo’s fractional derivative in non separable Banach spaces under Filippov type assumptions and we prove the existence of solutions. MSC: 34A60, 26A33, 34B15 keywords: fractional derivative, fractional semilinear differential inclusion, Lusin measurable multifunctions.

and Applied Analysis 3 is called the Riemann-Liouville fractional integral of h of order α > 0 when the right side exists. Here Γ is the usual Gamma function

Let Ω ⊂ RN be the upper half strip with a hole. In this paper, we show there exists a positive higher energy solution of semilinear elliptic equations in Ω and describe the dynamic systems of solutions of equation (1) in various Ω. We also show there exist at least two positive solutions of perturbed semilinear elliptic equations in Ω.