On a double phase problem with sublinear and superlinear nonlinearities

Abstract

In this paper, we study a class of double-phase problems with sub-critical growth. Some new criteria to guarantee that the existence and multiplicity results for the considered problem is established by using variational methods and critical point theory.

Keywords:

• Double phase problem
• variational method
• multiple critical points

AMS Subject Classifications:

• 35J60
• 35J70
• 35D30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the Fundamental Research Funds for the Central Universities (nos. DL12BC10, 3072020CF2401), the New Century Higher Education Teaching Reform Project of Heilongjiang Province in 2012 (no. JG2012010012), the Humanities and Social Sciences Foundation of the Educational Commission of Heilongjiang Province of China (no. 12544026).