Fast decaying solutions of Lane-Emden equations involving nonhomogeneous potential

TL;DR

This paper investigates positive solutions to a Lane-Emden equation with a nonhomogeneous potential, constructing a sequence of solutions that decay rapidly at infinity, expanding understanding of such equations with variable potentials.

Contribution

The paper introduces a method to construct a sequence of fast decaying positive solutions for Lane-Emden equations with nonhomogeneous potentials, under specific conditions.

Findings

Established existence of fast decaying solutions

Constructed a sequence of solutions with specific decay properties

Extended previous results to nonhomogeneous potentials

Abstract

We are interested in studying positive solutions of Lane-Emden equation $$ -\Delta u= V u^p\quad {\rm in}\quad \mathbb{R}^N\setminus\{0\}, $$ where $V$ is a nonhomogeneous potential satisfying some extra hypotheses. We construct a sequence of fast decaying solutions.