Heisenberg 群上 Kohn-Laplace 方程解的存在性——献给陈化教授 70 寿辰

Abstract

Abstract:

In this paper, we investigate, via variational methods, the existence of positive solution to a class of degenerate partial differential equations on the Heisenberg group involving critical Sobolev growth and logarithmic nonlinearity. In contrast to the classical perturbation term $\lambda u$ appearing in the [Brézis H, Nirenberg L. Comm Pure Appl Math, 1983, 36(4): 437-477], the logarithmic nonlinearity $\lambda u \log u^2$ leads to a weaker constraint on the parameter, yielding an improved existence result in the critical case.

Key words: Heisenberg group, critical Sobolev exponent, logarithmic nonlinearity, variational methods

CLC Number:

O175

Ming Zhang. Existence of Solution to the Kohn-Laplace Equation on the Heisenberg Group[J].Acta mathematica scientia,Series A, 2026, 46(2): 669-682.

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Existence of Solution to the Kohn-Laplace Equation on the Heisenberg Group

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