Combined effects in nonlinear problems arising in the study of anisotropic continuous media

TL;DR

This paper investigates nonlinear Lane-Emden-Fowler equations with variable potentials in anisotropic media, employing monotonicity and variational methods to establish existence results and analyze complex nonlinear interactions.

Contribution

It introduces a combined analytical approach for nonlinear anisotropic problems, extending previous methods to handle variable potentials and complex nonlinearities.

Findings

Established existence of solutions for the nonlinear problem.

Developed a novel combination of monotonicity and variational techniques.

Extended previous results to more general anisotropic media.

Abstract

The paper deals with the study of a Lane-Emden-Fowler equation with Dirichlet boundary condition and variable potential functions. The analysis developed in this paper combines monotonicity methods with variational arguments. Remark (April 21, 2020): Our results were later studied also by D.-P. Covei, Quasilinear problems with the competition between convex and concave nonlinearities and variable potentials, Internat. J. Math. 24:1 (2013), art. 1350005), arXiv:1104.4626v1.