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Multiple solutions to a Caffarelli-Kohn-Nirenberg type equation with asymptotically linear term

Benjin Xuan
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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.

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Benjin Xuan. 2004-04-02. Multiple solutions to a Caffarelli-Kohn-Nirenberg type equation with asymptotically linear term. https://arxiv.org/abs/math/0404038

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