On a class of double phase problem with nonlinear boundary conditions

Abstract

The existence of nontrivial solutions of the double phase problem with nonlinear boundary value condition is an important quasilinear problem: we use variational techniques and sum decomposition of a space $ W_0^{1, \xi}(\Omega) $ to prove the existence of infinitely many solutions of the problem considered. Moreover, our conditions are suitable and different from those considered previously.

Keywords

• double phase problem
• nonlinear boundary condition
• variational method
• infinitely many solutions
• sign-changing potential