Global bifurcation for nonlinear equations

• Published in: Nonlinear analysis Vol. 69; no. 8; pp. 2362 - 2368
• Main Authors: Kim, In-Sook, Kim, Yun-Ho
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 15.10.2008; Elsevier
• Subjects: [formula omitted]-Laplacian; Bifurcation; Exact sciences and technology; Functional analysis; Mathematical analysis; Mathematics; Nonlinear equation; Sciences and techniques of general use; Weighted Sobolev spaces; 35B32; Bifurcation; Nonlinear equation; 47J05; p -Laplacian; Weighted Sobolev spaces; p-Laplacian; Sobolev space; Nonlinear analysis; Eigenvalue; Boundary condition; Non linear equation; P laplacian; Mathematical model
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2007.08.013

Using a bifurcation result on noncompact branches of solutions in an abstract setting, we establish the existence of global bifurcation for the following nonlinear equation − div ( a | ∇ u | p − 2 ∇ u ) − μ 0 b | u | p − 2 u = q ( λ , x , u , ∇ u ) subject to Dirichlet boundary conditions under certain assumptions on a , b and q when μ 0 is not an eigenvalue of the above divergence form.