Summary: Maximum principles and nonexistence results for
radial solutions to equations involving p-Laplacian
, Agnieszka Kalamajska
We obtain the variant of maximum principle for radial solutions of, possibly
singular, p-harmonic equations of the form -a(|x|)p(w) + h(|x|, w, w(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, p-Laplace equation, singular
The study of the so-called 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