8 papers · 1 filter
Liouville theorem and a priori estimates of radial solutions for a non-cooperative elliptic system
Pavol Quittner
Liouville theorems for scaling invariant nonlinear elliptic systems (saying that the system does not possess nontrivial entire solutions) guarantee a priori estimates of solutions…
An optimal Liouville theorem for the linear heat equation with a nonlinear boundary condition
Pavol Quittner
Liouville theorems for scaling invariant nonlinear parabolic problems in the whole space and/or the halfspace (saying that the problem does not posses positive bounded solutions de…
Optimal Liouville theorems for superlinear parabolic problems
Pavol Quittner
Liouville theorems for scaling invariant nonlinear parabolic equations and systems (saying that the equation or system does not possess positive entire solutions) guarantee optimal…
Entire and ancient solutions of a supercritical semilinear heat equation
Peter Poláčik, Pavol Quittner
We consider the semilinear heat equation on . Assuming that and is greater than the Sobolev critical exponent , we examine ent…
On the multiplicity of self-similar solutions of the semilinear heat equation
Peter Poláčik, Pavol Quittner
In studies of superlinear parabolic equations \begin{equation*} u_t=Δu+u^p,\quad x\in {\mathbb R}^N,\ t>0, \end{equation*} where , backward self-similar solutions play an impo…
Uniqueness of singular self-similar solutions of a semilinear parabolic equation
Pavol Quittner
We study the uniqueness of singular radial (forward and backward) self-similar positive solutions of the equation where $p\geq(n+2)/(…