Zobrazeno 1 - 10
of 104
pro vyhledávání: '"Quittner, Pavol"'
Autor:
Quittner, Pavol, Souplet, Philippe
We establish Liouville type theorems in the whole space and in a half-space for parabolic problems without scale invariance. To this end, we employ two methods, respectively based on the corresponding elliptic Liouville type theorems and energy estim
Externí odkaz:
http://arxiv.org/abs/2409.20049
Autor:
Quittner, Pavol, Souplet, Philippe
We give applications of known and new Liouville type theorems to universal singularity and decay estimates for non scale invariant elliptic problems, including Lane-Emden and Schr\"odinger type systems. This applies to various classes of nonlineariti
Externí odkaz:
http://arxiv.org/abs/2407.04154
Autor:
Quittner, Pavol
This paper deals with necessary and sufficient conditions for weak and strong minimizers of functionals $\Phi(u)=\int_a^b f(x,u(x),u'(x))\,dx$, where $u\in C^1([a,b],{\mathbb R}^N)$. We first derive conditions which are simpler than the known ones, a
Externí odkaz:
http://arxiv.org/abs/2205.08765
Autor:
Quittner, Pavol
Liouville theorems for scaling invariant nonlinear elliptic systems (saying that the system does not possess nontrivial entire solutions) guarantee a priori estimates of solutions of related, more general systems. Assume that $p=2q+3>1$ is Sobolev su
Externí odkaz:
http://arxiv.org/abs/2108.13727
Autor:
Quittner, Pavol
Liouville theorems for scaling invariant nonlinear parabolic equations and systems (saying that the equation or system does not possess nontrivial entire solutions) guarantee optimal universal estimates of solutions of related initial and initial-bou
Externí odkaz:
http://arxiv.org/abs/2108.13723
Autor:
Quittner, Pavol
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 defined for all times $t\in(-\infty,\infty)$) guarantee optimal estimate
Externí odkaz:
http://arxiv.org/abs/2009.13923
Autor:
Quittner, Pavol
Liouville theorems for scaling invariant nonlinear parabolic equations and systems (saying that the equation or system does not possess positive entire solutions) guarantee optimal universal estimates of solutions of related initial and initial-bound
Externí odkaz:
http://arxiv.org/abs/2003.13223
Autor:
Poláčik, Peter, Quittner, Pavol
We consider the semilinear heat equation $u_t=\Delta u+u^p$ on ${\mathbb R}^N$. Assuming that $N\ge 3$ and $p$ is greater than the Sobolev critical exponent $(N+2)/(N-2)$, we examine entire solutions (classical solutions defined for all $t\in {\mathb
Externí odkaz:
http://arxiv.org/abs/1907.07873
Autor:
Poláčik, Peter, Quittner, Pavol
In studies of superlinear parabolic equations \begin{equation*} u_t=\Delta u+u^p,\quad x\in {\mathbb R}^N,\ t>0, \end{equation*} where $p>1$, backward self-similar solutions play an important role. These are solutions of the form $ u(x,t) = (T-t)^{-1
Externí odkaz:
http://arxiv.org/abs/1906.11159