Bifurcation and Multiplicity Results for Elliptic Problems with Subcritical Nonlinearity on the Boundary

2021/05/25 by Shalmali Bandyopadhyay, Bandyopadhyay, Shalmali, Maya Chhetri +7 · 2 citations
Computer Science · Mathematics · #35J15 #35J61 #35J65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2105.11890

openalex publication_date 2021/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Positive solutions of elliptic systems with superlinear nonlinearities on the boundary
• Numerical Approximation and Bifurcation Results for an Elliptic Problem with Superlinear Subcritical Nonlinearity on the Boundary

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