In this paper, we study some new connections between parabolic Liouvilletype theorems and local and global properties of nonnegative classical solutions to superlinear parabolic problems, with or… (More)

The main purpose of this paper is to improve the result of Cazenave and Lions in [CL] by proving the same a priori bound for p < pS . The proof of our result is based on the original proof of… (More)

We consider the dynamics of the semiflow associated with a class of semilinear parabolic problems on a smooth bounded domain, posed with homogeneous Dirichlet boundary conditions. The distinguishing… (More)

We investigate stationary solutions and asymptotic behaviour of solutions of two boundary value problems for semilinear parabolic equations. These equations involve both blow up and damping terms and… (More)

In this paper, we study some new connections between Liouville-type theorems and local properties of nonnegative solutions to superlinear elliptic problems. Namely, we develop a general method for… (More)

We consider the semilinear parabolic equation ut = ∆u + up on RN , where the power nonlinearity is subcritical. We first address the question of existence of entire solutions, that is, solutions… (More)

A detailed study of abstract semilinear evolution equations of the form u̇+Au = μ(u) is undertaken, where −A generates an analytic semigroup and μ(u) is a Banach space valued measure depending on the… (More)

We study asymptotic behavior of global positive solutions of the Cauchy problem for the semilinear parabolic equation ut = ∆u + up in RN , where p > 1 + 2/N , p(N − 2) ≤ N + 2. The initial data are… (More)