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A sharp estimate and change on the dimension of the attractor for Allen-Cahn equations
Nikos I. Karachalios, Nikos B. Zographopoulos
We consider the semilinear reaction diffusion equation , in a bounded domain . We assume the standard Allen-Cahn-type nonl…
The semiflow of a reaction diffusion equation with a singular potential
Nikos I. Karachalios, Nikos B. Zographopoulos
We study the semiflow defined by a semilinear parabolic equation with a singular square potential . It is known that the Hardy-Poincaré inequal…
On the Dynamics of a Degenerate Parabolic Equation: Global Bifurcation of Stationary States and Convergence
Nikos I. Karachalios, Nikos B. Zographopoulos
We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the e…
On Neumann superlinear elliptic problems
Nikolaos Halidias
In this paper we are going to show the existence of a nontrivial solution to the following model problem, \begin{equation*} \left\{\begin{array}{lll} -Δ(u) = 2uln(1+u^2)+\frac{|u|^…
Landesman-Laser Conditions and Quasilinear Elliptic Problems
Nikolaos Halidias
In this paper we consider two elliptic problems. The first one is a Dirichlet problem while the second is Neumann. We extend all the known results concerning Landesman-Laser condit…
Existence result for a Neumann problem
Nikolaos Halidias
In this paper we are going to show the existence of a nontrivial solution to the following model problem, $\{\begin{array}{lll} - Δ(u) = 2uln(1+u^2)+\frac{|u|^2}{1+u^2}2u+usin(u) {…