Multiple solutions for an elliptic system with indefinite Robin boundary conditions

Abstract

Multiplicity of solutions is proved for an elliptic system with an indefinite Robin boundary condition under an assumption that links the linearisation at 0 and the eigenvalues of the associated linear scalar operator. Our result is based on a precise calculation of the topological degree of a suitable fixed point operator over large and small balls.

Keywords

• nonlinear elliptic systems
• indefinite robin condition
• multiplicity of solutions
• topological degree
• 35j57
• 35j60