Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Positive solutions for the p-Laplacian: application of the fibrering method

Pavel Drábeka1 and Stanislav I. Pohozaeva2

a1 Department of Mathematics, University of West Bohemia, P.O. Box 314, 323 23 Plzeň, Czech Republic e-mail>: pdrabek@kma.zcu.cz

a2 Steklov Mathematical Institut, Russian Academy of Sciences, Vavilova 42, 117 966 Moscow, Russia e-mail: pohzaev@class.mi.ras.ru

Abstract

Using the fibrering method, we prove the existence of multiple positive solutions of quasilinear problems of second order. The main part of our differential operator is p-Laplacian and we consider solutions both in the bounded domain Ω⊂ℝN and in the whole of ℝN. We also prove nonexistence results.

(Received October 20 1995)

(Revised April 23 1996)