Bounded Solutions of Elliptic BVPs in Exterior Domain

ABSTRACT

The aim of this paper is to answer the question: when the Dirichlet problem for a certain partial differential equations (PDE) of elliptic type considered in unbounded domain possess at least one (notrivial) non-negative solution. We also investigate the continuous dependence on functional parameters of these solutions. Our approach is based on variational methods.

Keywords:

• Dependence on functional parameters
• Duality method
• Euler-Lagrange equation
• Variational principle

Mathematics Subject Classification 1991:

• 35B18
• 35C25
• 49J05