A nonlinear boundary value problem containing nonstandard boundary conditions

摘要

In this paper, we consider a second-order nonlinear elliptic boundary value problem (BVP) on a bounded domain Ω⊂RN, with nonstandard boundary conditions (BCs). More precisely, at some boundary part, we impose a Dirichlet BC containing an unknown additive constant, accompanied of a nonlocal (integral) Neumann side condition. As an auxiliary problem, we first study the linear case, which, moreover, has practical relevance itself. Leaning upon the results obtained, we prove the existence and uniqueness of a solution to the nonlinear BVP considered, using, in particular, the maximum principle.