A proof for the conjecture on superlinear problems with Ambrosetti-Rabinowitz condition
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.
Cite
@article{arxiv.2601.14825,
title = {A proof for the conjecture on superlinear problems with Ambrosetti-Rabinowitz condition},
author = {Chong Li and Shujie Li},
journal= {arXiv preprint arXiv:2601.14825},
year = {2026}
}