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Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach

100%

Ćwiszewski A.

Open Mathematics

2011

tom 9

nr 2

244-268

A translation along trajectories approach together with averaging procedure and topological degree are used to derive effective criteria for existence of periodic solutions for nonautonomous evolution equations with periodic perturbations. It is shown that a topologically nontrivial zero of the averaged right hand side is a source of periodic solutions for the equations with increased frequencies. Our setting involves equations on closed convex cones, therefore it enables us to study positive solutions of nonlinear parabolic partial differential equations.

Some global results for nonlinear fourth order eigenvalue problems

68%

Aliyev Z.

Open Mathematics

2014

tom 12

nr 12

1811-1828

In this paper, we consider the nonlinear fourth order eigenvalue problem. We show the existence of family of unbounded continua of nontrivial solutions bifurcating from the line of trivial solutions. These global continua have properties similar to those found in Rabinowitz and Berestycki well-known global bifurcation theorems.

Ograniczanie wyników

2 Open Mathematics

1 Aliyev Z.

1 Ćwiszewski A.

1 2014

1 2011

Wyniki wyszukiwania

Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach

Some global results for nonlinear fourth order eigenvalue problems