Singular (p, q)-equations with superlinear reaction and concave boundary condition

Abstract

We consider a parametric nonlinear elliptic problem driven by the sum of a p-Laplacian and of a q-Laplacian (a $(p,q)$-equation) with a singular and $(p-1)$-superlinear reaction and a Robin boundary condition with $(q-1)$-sublinear boundary term $(q<p)$. So, the problem has the combined effects of singular, concave and convex terms. We look for positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.

Keywords:

• Concave and convex nonlinearities
• singular term
• nonlinear regularity theory
• nonlinear maximum principle
• comparison principles
• truncation $(p,q)$-Laplacian

2010 Mathematics Subject Classifications:

• 35J75
• 35J92
• 35P30

Disclosure statement

No potential conflict of interest was reported by the author(s).