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Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N

  • Deepak Kumar Mahanta , Tuhina Mukherjee EMAIL logo and Abhishek Sarkar
Published/Copyright: March 26, 2024

Abstract

In this paper, we deal with the existence of nontrivial nonnegative solutions for a ( p , N ) -Laplacian Schrödinger–Kirchhoff problem in N with singular exponential nonlinearity. The main features of the paper are the ( p , N ) growth of the elliptic operators, the double lack of compactness, and the fact that the Kirchhoff function is of degenerate type. To establish the existence results, we use the mountain pass theorem, the Ekeland variational principle, the singular Trudinger–Moser inequality, and a completely new Brézis–Lieb-type lemma for singular exponential nonlinearity.

MSC 2020: 35D30; 35J60; 35J92

Communicated by Christopher D. Sogge


Funding statement: Deepak Kumar Mahanta would like to express his heartfelt gratitude to the DST INSPIRE Fellowship DST/INSPIRE/03/2019/000265 supported by the Government of India. Tuhina Mukherjee gratefully thanks the assistance of the Start up Research Grant from DST-SERB, sanction no. SRG/2022/000524. Abhishek Sarkar was supported by the DST-INSPIRE Grant DST/INSPIRE/04/2018/002208 sponsored by the Government of India.

Acknowledgements

The authors would like to thank anonymous referee for his/her comments and suggestions which has helped to enhance quality of the paper.

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Received: 2023-11-13
Revised: 2024-03-07
Published Online: 2024-03-26
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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