AMBROSETTI-PRODI PROBLEM WITH DEGENERATE POTENTIAL AND NEUMANN BOUNDARY CONDITION

作者：Repovs Dusan D.^*

来源：Electronic Journal of Differential Equations, 2018, 41.

• Ambrosetti-Prodi problem
• degenerate potential
• topological degree
• anisotropic continuous media

We study the degenerate elliptic equation
-div(vertical bar x vertical bar(alpha)del u)=f(u)+t phi(x)+h(x)
in a bounded open set Omega with homogeneous Neumann boundary condition, where alpha is an element of(0,2) and f has a linear growth. The main result establishes the existence of real numbers t(*) and t* such that the problem has at least two solutions if t <= t(*), there is at least one solution if t(*)t*. The proof combines a priori estimates with topological degree arguments.

• 出版日期2018-2-6