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arXiv · 2601.14825

A proof for the conjecture on superlinear problems with Ambrosetti-Rabinowitz condition

Chong Li·Shujie Li
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Abstract

This paper is devoted to exploring a new minimax approach by introducing a characteristic mapping family which is invariant under the smooth descending flow for initial value. The minimax approach is self-contained, and its features are markedly different from standard ones, as it identifies the existence of critical points and intrinsically presents a lower-bound estimate for the generalized Morse index at the corresponding critical point. This quantity can be effectively viewed as an alternative to the group action. As applications, under the Ambrosetti-Rabinowitz condition we offer a positive answer to the long-standing open problem on the existence of infinitely many distinct solutions for superlinear elliptic equations without symmetric hypothesis.

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Chong Li, Shujie Li. 2026-01-21. A proof for the conjecture on superlinear problems with Ambrosetti-Rabinowitz condition. https://arxiv.org/abs/2601.14825

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