Existence of solutions to equations of N-Laplacian type with Trudinger–Moser nonlinearities

Abstract

In this paper, using a fixed point result, we establish sufficient conditions for the existence of solutions to the nonuniformly elliptic equation of the formHere, is a positive parameter, the potential can change sign, may be unbounded in , the nonlinearity is possibly discontinuous and may exhibit exponential critical growth, and belongs to the dual of an appropriated function space.

Keywords:

• critical growth
• Trudinger–Moser inequality
• fixed point result
• discontinuous nonlinearity

AMS Subject Classifications:

• 35J92
• 47H10
• 35B33