Document Type
Article
Publication Date
12-5-2024
Published In
Journal Of Differential Equations
Abstract
We consider an elliptic problem with nonlinear boundary condition involving nonlinearity with superlinear and subcritical growth at infinity and a bifurcation parameter as a factor. We use re-scaling method, degree theory and continuation theorem to prove that there exists a connected branch of positive solutions bifurcating from infinity when the parameter goes to zero. Moreover, if the nonlinearity satisfies additional conditions near zero, we establish a global bifurcation result, and discuss the number of positive solution(s) with respect to the parameter using bifurcation theory and degree theory.
Keywords
Elliptic problem, Nonlinear boundary conditions, Superlinear and subcritical, Local bifurcation, Degree theory, Global bifurcation
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
S. Bandyopadhyay, M. Chhetri, B. B. Delgado, Nsoki Mavinga, and R. Pardo.
(2024).
"Bifurcation And Multiplicity Results For Elliptic Problems With Subcritical Nonlinearity On The Boundary".
Journal Of Differential Equations.
Volume 411,
28-50.
DOI: 10.1016/j.jde.2024.07.041
https://works.swarthmore.edu/fac-math-stat/328
Comments
This work is freely available under a Creative Commons license.