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Impulsive boundary value problems for p ( t ) -Laplacian’s via critical point theory

Marek Galewski, Donal O'Regan (2012)

Czechoslovak Mathematical Journal

In this paper we investigate the existence of solutions to impulsive problems with a p ( t ) -Laplacian and Dirichlet boundary value conditions. We introduce two types of solutions, namely a weak and a classical one which coincide because of the fundamental lemma of the calculus of variations. Firstly we investigate the existence of solution to the linear problem, i.e. a problem with a fixed rigth hand side. Then we use a direct variational method and next a mountain pass approach in order to get the existence...

Impulsive periodic boundary value problem

Jan Draessler (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the paper we consider the impulsive periodic boundary value problem with a general linear left hand side. The results are based on the topological degree theorems for the corresponding operator equation ( I - F ) u = 0 on a certain set Ω that is established using properties of strict lower and upper functions of the boundary value problem.

Infinitely many solutions of a second-order p -Laplacian problem with impulsive condition

Libo Wang, Weigao Ge, Minghe Pei (2010)

Applications of Mathematics

Using the critical point theory and the method of lower and upper solutions, we present a new approach to obtain the existence of solutions to a p -Laplacian impulsive problem. As applications, we get unbounded sequences of solutions and sequences of arbitrarily small positive solutions of the p -Laplacian impulsive problem.

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