Startseite Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N
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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 und Abhishek Sarkar
Veröffentlicht/Copyright: 26. März 2024
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 37 Heft 2

Abstract

In this paper, we deal with the existence of nontrivial nonnegative solutions for a ( p , N ) -Laplacian Schrödinger–Kirchhoff problem in ℝ 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.

Keywords: Schrödinger–Kirchhoff equations; Trudinger–Moser inequality; Ekeland variational principle; mountain pass theorem; 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

Artikel in diesem Heft

  1. Frontmatter
  2. Triangles with one fixed side–length, a Furstenberg-type problem, and incidences in finite vector spaces
  3. Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in ℝ N
  4. Estimates of Picard modular cusp forms
  5. Some q-supercongruences from a q-analogue of Watson's 3 F 2 summation
  6. Existence of strong solutions for one-dimensional reflected mixed stochastic delay differential equations
  7. Free groups generated by two unipotent maps
  8. Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N
  9. Colored multizeta values in positive characteristic
  10. Simultaneous nonvanishing of central L-values with large level
  11. Laplace convolutions of weighted averages of arithmetical functions
  12. Cohomological properties of maximal pro-p Galois groups that are preserved under profinite completion
  13. On the geometric trace of a generalized Selberg trace formula
  14. Elementary properties of free lattices
  15. Weighted estimates for product singular integral operators in Journé’s class on RD-spaces
  16. Small generators of abelian number fields
  17. Pointwise convergence and nonlinear smoothing of the generalized Zakharov–Kuznetsov equation
  18. Weighted bilinear multiplier theorems in Dunkl setting via singular integrals
https://doi.org/10.1515/forum-2023-0407
Schlagwörter für diesen Artikel
Schrödinger–Kirchhoff equations; Trudinger–Moser inequality; Ekeland variational principle; mountain pass theorem; exponential nonlinearity

Artikel in diesem Heft

  1. Frontmatter
  2. Triangles with one fixed side–length, a Furstenberg-type problem, and incidences in finite vector spaces
  3. Existence and multiplicity of solutions for fractional Schrödinger-p-Kirchhoff equations in ℝ N
  4. Estimates of Picard modular cusp forms
  5. Some q-supercongruences from a q-analogue of Watson's 3 F 2 summation
  6. Existence of strong solutions for one-dimensional reflected mixed stochastic delay differential equations
  7. Free groups generated by two unipotent maps
  8. Degenerate Schrödinger--Kirchhoff {(p,N)}-Laplacian problem with singular Trudinger--Moser nonlinearity in ℝ N
  9. Colored multizeta values in positive characteristic
  10. Simultaneous nonvanishing of central L-values with large level
  11. Laplace convolutions of weighted averages of arithmetical functions
  12. Cohomological properties of maximal pro-p Galois groups that are preserved under profinite completion
  13. On the geometric trace of a generalized Selberg trace formula
  14. Elementary properties of free lattices
  15. Weighted estimates for product singular integral operators in Journé’s class on RD-spaces
  16. Small generators of abelian number fields
  17. Pointwise convergence and nonlinear smoothing of the generalized Zakharov–Kuznetsov equation
  18. Weighted bilinear multiplier theorems in Dunkl setting via singular integrals
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