Antiperiodic solutions for semilinear evolution equations

On approximate solutions of semilinear evolution equations

A general framework is presented to discuss the approximate solutions of an evolution equation in a Banach space, with a linear part generating a semigroup and a sufficiently smooth nonlinear part. A theorem is presented, allowing to infer from an approximate solution the existence of an exact solution. According to this theorem, the interval of existence of the exact solution and the distance ...

Existence of Mild Solutions for Nonlocal Semilinear Fractional Evolution Equations

In this paper, we investigate a class of semilinear fractional evolution equations with nonlocal initial conditions given by (1) ⎧⎨ ⎩ dqu(t) dtq = Au(t)+(Fu)(t), t ∈ I, u(0)+g(u) = u0, where 0 < q< 1 , I is a compact interval. Sufficient conditions for the existence of mild solutions for the equation (1) are derived. The main tools include Laplace transform, Arzela-Ascoli’s Theorem, Schauder’s ...

Existence of Solutions of Abstract Fractional Impulsive Semilinear Evolution Equations

In this paper we prove the existence of solutions of fractional impulsive semilinear evolution equations in Banach spaces. A nonlocal Cauchy problem is discussed for the evolution equations. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the theory.

Local and global nonexistence of solutions to semilinear evolution equations

For a fixed p and σ > −1, such that p > max{1, σ + 1}, one main concern of this paper is to find sufficient conditions for non solvability of ut = −(−∆) β 2 u− V (x)u+ th(x)u +W (x, t), posed in ST := R × (0, T ), where 0 < T < +∞, (−∆) β 2 with 0 < β ≤ 2 is the β/2 fractional power of the −∆, and W (x, t) = tw(x) ≥ 0. The potential V satisfies lim sup|x|→+∞ |V (x)||x| < +∞, for some positive a...

Boundedness of solutions for semilinear duffing equations