Inclusion problems via subsolution–supersolution method with applications to hemivariational inequalities

Abstract

Existence and location of solutions to a Dirichlet problem driven by (p, q)-Laplacian and containing a (convection) multivalued term fully depending on the solution and its gradient are established through the method of subsolution–supersolution. This result extends preceding works, in particular improving the growth condition for the lower order terms and allowing multivalued nonlinearities. A criterion for the existence of positive solutions with a priori estimates is obtained. Finally, an application to hemivariational inequalities is given.

Keywords:

• Quasilinear elliptic inclusion
• (p
•  q)-Laplacian
• gradient dependence
• subsolution
• supersolution

AMS Subject Classifications:

• 35J92
• 35J25

Acknowledgements

The authors are grateful to the referees for their helpful comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Project supported by National Natural Science Foundation of China [grant number 11671101]; Special Funds of Guangxi Distinguished Experts Construction Engineering.