Fixed point theorems for multivalued operators and application to discontinuous quasilinear BVP's

In this article, we prove an abstract fixed point theorem for increasing multivalued operators in ordered topological spaces, which provides an efficient tool to obtain qualitative results on the solution set of discontinuous quasilinear elliptic boundary value problems. In particular, we are able to show the existence of extremal solutions of such problems.

Keywords:

• Fixed Point Theorem
• Increasing Multivalued Operators
• Ordered Topological Space
• Quasilinear Elliptic Boundary Value Problem
• Discontinuous Nonlinearity
• Extremal Solutions
• Ams Subject Classifications: 35j65
• 35r05
• 47h04
• 47h10