Inhomogeneous Neumann problem with critical Sobolev exponent

Abstract

We investigate the solvability of the inhomogeneous Neumann problem involving the critical Sobolev exponent. In particular, we discuss the impact of the shape of the graph of the coefficient of the critical exponent on the existence of a solution. We prove the existence of at least two solutions for belonging to a bounded interval . We establish the existence of at least two solutions for a modified problem, that is, with the operator replaced by .

Keywords

• neumann problem
• critical sobolev exponent
• multiple solutions
• minimal solutions
• indefinite weights