Existence of solutions for nonlinear parabolic problems

Nikolaos Halidias; Nikolaos S. Papageorgiou

Displaying similar documents to “Existence of solutions for nonlinear parabolic problems”

Periodic problems and problems with discontinuities for nonlinear parabolic equations

Tiziana Cardinali, Nikolaos S. Papageorgiou (2000)

Czechoslovak Mathematical Journal

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In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and...

Transition from decay to blow-up in a parabolic system

Pavol Quittner (1998)

Archivum Mathematicum

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We show a locally uniform bound for global nonnegative solutions of the system $u_{t} = Δ u + u v - b u$ , $v_{t} = Δ v + a u$ in $(0, + \infty) \times Ω$ , $u = v = 0$ on $(0, + \infty) \times \partial Ω$ , where $a > 0$ , $b \geq 0$ and $Ω$ is a bounded domain in $ℝ^{n}$ , $n \leq 2$ . In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.

Quasilinear elliptic problems with multivalued terms

Nikolaos Halidias, Nikolaos S. Papageorgiou (2000)

Czechoslovak Mathematical Journal

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We study the quasilinear elliptic problem with multivalued terms.We consider the Dirichlet problem with a multivalued term appearing in the equation and a problem of Neumann type with a multivalued term appearing in the boundary condition. Our approach is based on Szulkin’s critical point theory for lower semicontinuous energy functionals.