2 citations · 2 across the 2 of their papers we have counts for
9 papers
Nondegeneracy of heteroclinic orbits for a class of potentials on the plane
Jacek Jendrej, Panayotis Smyrnelis
In the scalar case, the nondegeneracy of heteroclinic orbits is a well-known property, commonly used in problems involving nonlinear elliptic, parabolic or hyperbolic P.D.E. On the…
A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores
Panayotis Smyrnelis
We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to…
Double layered solutions to the extended Fisher-Kolmogorov P.D.E.
Panayotis Smyrnelis
We construct double layered solutions to the extended Fisher-Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a s…
Vortex solutions in the Ginzburg-Landau-Painlevé theory of phase transition
Panayotis Smyrnelis
The extended Painlevé P.D.E. system , , , is obtained by multiplying by the linear t…
Connecting orbits in Hilbert spaces and applications to P.D.E
Panayotis Smyrnelis
We prove a general theorem on the existence of heteroclinic orbits in Hilbert spaces, and present a method to reduce the solutions of some P.D.E. problems to such orbits. In our fi…
Blowing up solutions of semilinear P.D.E. with convex potentials
Panayotis Smyrnelis
We consider convex potentials vanishing at and growing sufficiently fast at . Given any open set with Lipschitz and compact bound…