Radial solutions for a p-Laplace equation involving nonlinearity terms

Abstract

Our main interest is to demonstrate the existence of at least one positive radial solution for the p-Laplacian problem $\{\begin{array}{ll}-div(|\mathrm{\nabla }u{|}^{p-2}\mathrm{\nabla }u)+R(x)|u{|}^{p-2}u=f(u)-g(u)& x\in B,\\ u>0& x\in B,\\ u=0& x\in \mathrm{\partial }B,\end{array}$ where B is the unit ball centred at the origin in ${\mathbb{R}}^n,n\ge 3$ and $p\ge 2$, via the variational method.

Keywords:

• Variational principle
• p-Laplace equation
• mountain pass theorem

AMS Subject Classifications:

• 49J24
• 49J52
• 54C60

Acknowledgements

The authors thank the anonymous reviewers for their careful reading of the paper and their many insightful comments and suggestions.

Disclosure statement

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