 
Summary: Maximum principles and nonexistence results for
radial solutions to equations involving pLaplacian
Tomasz Adamowicz
, Agnieszka Kalamajska
Abstract
We obtain the variant of maximum principle for radial solutions of, possibly
singular, pharmonic equations of the form a(x)p(w) + h(x, w, w(x) ·
x
x ) = (w), as well as for solutions of the related ODE. We show that for the
considered class of equations local maximas of w form a monotone sequence in x
and constant sign solutions are monotone. The results are applied to nonexistence
and nonlinear eigenvalue problems and generalize our previous work.
Mathematics Subject Classification (2000). Primary: 35B50; Secondary: 35P30, 34C11.
Key words and phrases: maximum principles, radial solutions, pLaplace equation, singular
elliptic PDE's.
1 Introduction
The study of the socalled nonlinear eigenvalue problems is one of the main areas of p
harmonic theory, e.g. [18, 22, 23, 32, 40, 42]. The starting point for such considerations
is the following equation
div( up2
