Bifurcation and blow-up results for equations with $p$-Laplacian and convex-concave nonlinearity

Abstract

This paper is concerned with the existence of global, blow-up and bifurcation solutions for parametrized families of elliptic and parabolic equations with $p$-Laplacian and concave-convex nonlinearity. The main results are obtained by means of a generalised Collatz-Wielandt formula.

Keywords

• concave–convex nonlinearity
• collatz–wielandt formula
• $p$-laplacian
• bifurcation
• blow up