Global bifurcation of the -Laplacian in
β Scribed by In-Sook Kim; Yun-Ho Kim
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 430 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
β¦ Synopsis
We study global bifurcation for the following nonlinear equation:
satisfying certain conditions on a, g, and f when Β΅ 0 is not an eigenvalue of the above divergence form. It is based on a bifurcation result on noncompact components of solutions for nonlinear operator equations.
π SIMILAR VOLUMES
We prove here bifurcation and existence results for a nonlinear elliptic system involving the p -Laplacian. We say that i is an eigenvalue of (E,) if there exists a nontrivial pair (u,v) E ( W i ' p ) 2 1991 Mathematics Subject Classification. 35; 35 G ; 35 J. Keywords and phrases. p -Laplacian, sy
and the associated problem with homogeneous principal part, < < py2 < < py2 ydiv a x Ωu Ωu sg x u u q f , x, u , 2 0 in R N and may be singular or degenerate at infinity, no growth restriction on Ε½ . a x, ΠΈ is postulated, and both f and g may change sign.
In this paper, we study the following p(x)-Laplacian equation: where β¦ β R N is bounded, Ξ» β₯ 0. Under suitable assumptions, we obtain the existence of global branches of solutions for the above problem via the subsolution-supersolution method.