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Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Center
 

Summary: Topological Methods in Nonlinear Analysis
Journal of the Juliusz Schauder Center
Volume 34, 2009, 1­20
ON A VARIANT OF THE MAXIMUM PRINCIPLE
INVOLVING RADIAL p-LAPLACIAN
WITH APPLICATIONS TO NONLINEAR
EIGENVALUE PROBLEMS
AND NONEXISTENCE RESULTS
Tomasz Adamowicz -- Agnieszka Kalamajska
Abstract. We obtain the variant of maximum principle for radial solu-
tions of p-harmonic equation -ap(w) = (w). As a consequence of this
result we prove monotonicity of constant sign solutions, analyze the sup-
port of the solutions and study their oscillations. The results are applied
to various type nonlinear eigenvalue problems and nonexistence theorems.
1. Introduction
Problems involving p-Laplace operator are subject of intensive studies as they
very well illustrate many of phenomena that occur in nonlinear analysis. Among
their applications are singular and nonsingular boundary value problems which
appear in various branches of mathematical physics. They arise as a model
example in the fluid dynamics ([18], [27], [28], Chapter 2 in [31], [55], [62]);

  

Source: Adamowicz, Tomasz - Matematiska Institutionen, Linköpings Universitet

 

Collections: Mathematics