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Bifurcation analysis of fractional Kirchhoff problems with singular exponential nonlinearity

  • Linlin Wang
  • , Yuming Xing*
  • *Corresponding author for this work
  • School of Mathematics, Harbin Institute of Technology

Research output: Contribution to journalArticlepeer-review

Abstract

This paper deals with the bifurcation results of (weak) solutions for the Kirchhoff fractional p-Laplacian equation (Formula presented.) where (Formula presented.) denotes the fractional operator, with sp = N, and the nonlinearity f exhibits the singular exponential growth at infinity. Moreover, the existence of unbounded components of (weak) solutions emanating from the trivial solution, is treated via the fix point result and the global bifurcation theorem due to Rabinowitz. Finally, the main feature of this paper consists of the existence of positive solutions to the above equation for λ small enough.

Original languageEnglish
Pages (from-to)885-902
Number of pages18
JournalComplex Variables and Elliptic Equations
Volume70
Issue number5
DOIs
StatePublished - 2025
Externally publishedYes

Keywords

  • 35B32
  • 35R11
  • 45G05
  • 47G20
  • Fractional Kirchhoff equation
  • global bifurcation
  • nonlinear eigenvalue problem
  • singular exponent nonlinearity

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