This paper is devoted to establishing local and global existence theorems for autonomous semilinear parabolic initial value problems. The local existence theorems do not require Lipchitz condition on nonlinear term. The global existence theorem is an extension of the well-known result of Fujita-Weissler for semilinear heat equations to general autonomous semilinear parabolic equations and systems.

We consider the pullback attractors for non-autonomous dynamical systems generated by stochastic lattice differential equations with non-autonomous deterministic terms. We first establish a sufficient condition for existence of pullback attractors of lattice dynamical systems with both non-autonomous deterministic and random forcing terms. As an application of the abstract theory, we prove the ...

at present paper, we establish the existence of pullback $mathcal{d}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $l^2(mathbb{r}^n)times l^2(mathbb{r}^n)$. in order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{d}$-absorbing set, is pullback $widehat{d}_0$-asymptotically compact.

Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

We construct an index theorem for smooth infinite economies that shows that generically the number of equilibria is odd. As a corollary, this gives a new proof of existence and gives conditions that guarantee global uniqueness of equilibria.