Bifurcation analysis of elliptic equations described by nonhomogeneous differential operators

Bifurcation analysis of elliptic equations described by nonhomogeneous differential operators

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In this article, we are concerned with a class of nonlinear partial differential elliptic equations with Dirichlet boundary data.The key feature of this paper consists in competition effects of two generalized differential operators, which extend the standard operators with variable exponent.This class of problems is motivated by phenomena Physical fitness of children and youth with asthma in comparison to the reference population arising in non-Newtonian fluids or image reconstruction, which deal with operators and nonlinearities with variable exponents.We establish an The influence of the circulation on surface temperature and precipitation patterns over Europe existence property in the framework of small perturbations of the reaction term with indefinite potential.

The mathematical analysis developed in this paper is based on the theory of anisotropic function spaces.Our analysis combines variational arguments with energy estimates.