A proof for the conjecture on superlinear problems with Ambrosetti-Rabinowitz condition
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909996788219904 |
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| author | Li, Chong Li, Shujie |
| author_facet | Li, Chong Li, Shujie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14825 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A proof for the conjecture on superlinear problems with Ambrosetti-Rabinowitz condition Li, Chong Li, Shujie Functional Analysis 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. |
| title | A proof for the conjecture on superlinear problems with Ambrosetti-Rabinowitz condition |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2601.14825 |