Multiple solutions to a
Caffarelli-Kohn-Nirenberg
type equation with
asymptotically linear term
Benjin Xuan University of Science and Technology of China, Hefei
Abstract.
In this paper, we study the existence of multiple solutions to a
Caffarelli-Kohn-Nirenberg type equation with asymptotically linear
term at infinity. In this case, the well-known
Ambrosetti-Rabinowtz type condition doesn't hold, hence it is
difficult to verify the classical (PS)$_c$ condition. To overcome
this difficulty, we use an equivalent version of Cerami's
condition, which allows the more general existence result.
Palabras claves. Caffarelli-Kohn-Nirenberg type equation, asymptotically linear,
Ambrosetti-Rabinowtz type condition, Cerami condition.
