Existence of solutions to a class of elliptic equations with nonstandard growth condition and zero order term

Abstract

The existence of bounded weak solutions, to a class of nonlinear elliptic equations with variable exponents, is investigated in this article. A uniform a priori L^{\mathrm{\infty }} estimate is obtained by the De Giorgi iterative technique. Thanks to the weak convergence method and Minty's trick, the existence result is proved through limit process.

Key words： Elliptic equations; variable exponents; De Giorgi iteration; Minty's trick

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. 11901131) and Youth science and technology talent growth project in Guizhou Province for ordinary institutions of higher learning (KY[2021]142).

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