<p style='text-indent:20px;'>In present paper, we deal with the behavior of a solution beyond occurrence wave breaking for modified periodic Coupled Camassa-Holm system. By introducing new set independent and dependent variables, which resolve all singularities due to possible breaking, this evolution system is rewritten as closed semilinear The local existence obtained fixed points contr...

A semilinear space S is a non-empty set of elements called points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every line contains at least two points. Two points p and q are said to be collinear if p 6ˆ q and if the pair f p; qg is contained in a line; the line containing two collinear points p and q will be denoted by pq...

Membrane computing is a relatively young but fast emerging bio-inspired computing paradigm, nowadays with many branches and applications. Its original computing model is the catalytic P system. Although it was proven already in 2005 that catalytic P systems with two catalysts are computationally universal [2], no simple example of such a P system generating a non-semilinear set was known. The p...

Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work. 

* Correspondence: lpzmath@yahoo. com.cn School of Mathematics, Yangzhou University, Yangzhou 225002, China Abstract This article is concerned with impulsive semilinear differential equations with nonlocal initial conditions in Banach spaces. The approach used is fixed point theorem combined with the technique of operator transformation. Existence results are obtained when the nonlocal item is L...

In this paper we prove the existence and uniqueness of the boundary layer solution to a semilinear eigenvalue problem consisting of a coupled system of two elliptic partial differential equations. Although the system is not quasimonotone, there exists a transformation to a quasimonotone system. For the transformed system we may and will use maximum (sweeping) principle arguments to derive point...

In this paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary condition and sign-changing potential. With the help of the Nehari manifold, we prove that the semilinear elliptic equation: −∆u+ u = λf(x)|u|q−2u in Ω, ∂u ∂ν = g(x)|u|p−2u on ∂Ω, has at least two nontrivial nonnegative solutions for λ is sufficiently small.