Sharp conditions for the existence of infinitely many positive solutions to $ q $-$ k $-Hessian equation and systems

Haitao Wan; Yongxiu Shi; Haitao Wan; Yongxiu Shi

doi:10.3934/era.2024234

Electronic Research Archive

2024, Volume 32, Issue 8: 5090-5108. doi: 10.3934/era.2024234

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Sharp conditions for the existence of infinitely many positive solutions to $ q $-$ k $-Hessian equation and systems

Haitao Wan ^,,
Yongxiu Shi

School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, China

Received: 05 April 2024 Revised: 02 July 2024 Accepted: 13 August 2024 Published: 26 August 2024

In this paper, only under the $ q $-$ k $-Keller–Osserman conditions, we consider the existence and global estimates of innumerable radial $ q $-$ k $-convex positive solutions to the $ q $-$ k $-Hessian equation and systems. Our conditions are strictly weaker than those in previous papers.
- $ q $-$ k $-Hessian problems,
- radial $ q $-$ k $-convex solutions,
- the existence of solutions
Citation: Haitao Wan, Yongxiu Shi. Sharp conditions for the existence of infinitely many positive solutions to $ q $-$ k $-Hessian equation and systems[J]. Electronic Research Archive, 2024, 32(8): 5090-5108. doi: 10.3934/era.2024234

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Abstract

In this paper, only under the $ q $-$ k $-Keller–Osserman conditions, we consider the existence and global estimates of innumerable radial $ q $-$ k $-convex positive solutions to the $ q $-$ k $-Hessian equation and systems. Our conditions are strictly weaker than those in previous papers.

References

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