The set of solutions for certain semilinear heat equations

Holomorphic Solutions of Semilinear Heat Equations

with φ ∈ L(R), where P is a polynomial vanishing at the origin and ∆ stands for the Laplacian with respect to x. The analyticity in time of the solutions of a semilinear heat equation has been considered by many authors. For example Ōuchi [2] treated the analyticity in time of the solutions of certain initial boundary value problems with bounded continuous initial functions, which include (1) i...

Global Solutions of Semilinear Heat Equations in Hilbert Spaces

The existence, uniqueness, regularity and asymptotic behavior of global solutions of semilinear heat equations in Hilbert spaces are studied by developing new results in the theory of one-parameter strongly continuous semigroups of bounded linear operators. Applications to special semilinear heat equations in L(R) governed by pseudo-differential operators are given.

Boundedness of solutions for semilinear duffing equations

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS

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...

Singular Solutions for some Semilinear Elliptic Equations

We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...