The Ground State Solutions for Kirchhoff-Schr¨odinger Type Equations with Singular Exponential Nonlinearities in RN*

Citation:

Yanjun LIU,Chungen LIU.The Ground State Solutions for Kirchhoff-Schr¨odinger Type Equations with Singular Exponential Nonlinearities in RN*[J].Chinese Annals of Mathematics B,2022,43(4):549~566
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Authors:

Yanjun LIU; Chungen LIU

Foundation:

National Natural Science Foundation of China (Nos. 11790271, 12171108, 12201089), Guangdong Basic and Applied basic Research Foundation (No. 2020A1515011019), Innovation and Development Project of Guangzhou University and Chongqing Normal University Foundation (No. 21XLB039).
Abstract: In this paper, the authors consider the following singular Kirchhoff-Schr¨odinger problem M Z RN |u|N + V (x)|u|N dx (N u + V (x)|u|N?2u) = f(x, u) |x|η in RN , (Pη) where 0 < η < N, M is a Kirchhoff-type function and V (x) is a continuous function with positive lower bound, f(x, t) has a critical exponential growth behavior at infinity.Combining variational techniques with some estimates, they get the existence of ground state solution for (Pη). Moreover, they also get the same result without the A-R condition.

Keywords:

Ground state solutions, Singular elliptic equations, Critical exponential growth, Kirchhoff-Schr¨odinger equations, Singular Trudinger-Moser inequality

Classification:

35J60, 35B33, 46E30
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