Localization of solutions for semilinear problems with poly-Laplace type operators

Abstract

The paper presents an abstract theory regarding the problems with semilinear operator equations involving iterates of a strongly monotone symmetric linear operator. We obtain existence and localization results of positive solutions for such problems using Krasnosel'skiĭ's technique and abstract Harnack inequality. In particular, we obtain results for problems with semilinear poly-Laplace operators.

Keywords:

• Krasnosel'skiĭ's technique
• fixed point
• Harnack inequality
• iterates of a symmetric linear operator
• poly-Laplace type operator

Maths:

• 47J05
• 47H10

Acknowledgments

The authors would like to thank the reviewer for careful reading of the manuscript and for valuable remarks and suggestions which led to an improved version of the paper.

Disclosure statement

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