We study S-asymptotically ω-periodic mild solutions of the semilinear Volterra equation u′(t) = (a ∗ Au)(t) + f(t, u(t)), considered in a Banach space X, where A is the generator of an (exponentially) stable resolvent family. In particular, we extend recent results for semilinear fractional integro-differential equations considered in [4] and for semilinear Cauchy problems of first order given ...

Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in RN with the Schauder-Tychonoff fixed point theorem as the principal tool. In many articles, the theorems of existence and multiple of positive entire solutions for a class semilinear elliptic equations are established. The results of the semilinear equations...

April 19, 2009 Version 1.0.2 Date 2007-07-13 Maintainer Deli Wang Author Deli Wang, Jian Huang Depends splines Title A two-way semilinear model for normalization and analysis of cDNA microarray data. Description twslm is for normalization of cDNA microarray data with the two-way semilinear model. Huber’s and Tukey’s bisquare weight functions are available for robust esti...

In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in usual set-up for dynamical systems generated by differential equations delay terms. This approach different from ones used previous published literature on memory, which carried out Dafermos transformation. As consequence, obtained results provide complete informatio...

We consider extended variants of spiking neural P systems and show how these extensions of the original model allow for easy proofs of the computational completeness of extended spiking neural P systems and for the characterization of semilinear sets and regular languages by finite extended spiking neural P systems (defined by having only finite checking sets in the rules assigned to the cells)...

We look at 1-region membrane computing systems which only use rules of the form , where is a catalyst, is a noncatalyst, and is a (possibly null) string of noncatalysts. There are no rules of the form . Thus, we can think of these systems as “purely” catalytic. We consider two types: (1) when the initial configuration contains only one catalyst, and (2) when the initial configuration contains m...

In this paper, we study the semilinear wave equation with lower order terms (damping and mass) power type nonlinearity $|u|^p$ on compact Lie groups. We will prove global in time existence of small data solutions evolution energy space without requiring any bounds for $p>1$. our approach, employ some results from Fourier analysis

In this paper, we introduce locally Lipschitz observation systems for nonlinear semigroups and show that they can be represented by an ‘admissible’ nonlinear output operator defined on a suitable subspace. In the semilinear case, this concept fits well to the Lebesgue extension known from linear system theory. Also in the semilinear case, we show robustness of exact observability near equilibri...

In this paper we consider the nonlinearly damped semilinear Petrovsky equation utt + 2u+ aut ut m−2 = bu u p−2 in a bounded domain, where a b > 0. We prove the existence of a local weak solution and show that this solution blows up in finite time if p > m and the energy is negative. We also show that the solution is global if m ≥ p.  2002 Elsevier Science