Ground State Solutions for the Schrödinger-Poisson-Slater Equation with Double Critical Exponents

doi:10.3969/j.issn.1006-8074.2026.01.005

Mathematical Theory and Applications ›› 2026, Vol. 46 ›› Issue (1): 72-.doi: 10.3969/j.issn.1006-8074.2026.01.005

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Ground State Solutions for the Schrödinger-Poisson-Slater Equation with Double Critical Exponents

Shao Yumi; Lei Chunyu^*

School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China

Online:2026-03-28 Published:2026-04-23
Contact: Lei Chunyu; E-mail: leichygzu@sina.cn
Supported by:
This work is supported by the National Natural Science Foundation of China (No. 12461024), the Science and Technology Foundation of

Guizhou Province (No. ZK[2024]059), and the Natural Science Research Project of Department of Education of Guizhou Province (No. QJJ2023062)

Abstract

Abstract: This paper is concerned with the Schr\"odinger-Poisson-Slater (SPS) equations incorporating both Coulomb-Sobolev and Sobolev critical exponents in $\mathbb{R}^3$. These double critical exponents, specifically 3 and 6, lead to the non-compactness of embeddings in the relevant function space. By utilizing the Pohozaev identity and the Br\'{e}zis-Lieb lemma, we show the existence of ground state solutions.

Key words: Schr?dinger-Poisson-Slater equation, Pohozaev identity, Coulomb-Sobolev inequality

Shao Yumi, Lei Chunyu. Ground State Solutions for the Schrödinger-Poisson-Slater Equation with Double Critical Exponents[J]. Mathematical Theory and Applications, 2026, 46(1): 72-.

Ground State Solutions for the Schrödinger-Poisson-Slater Equation with Double Critical Exponents

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