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Global bifurcation for generalized Laplacian operators

In-Sook Kim
대한수학회 (The Korean Mathematical Society)|2009.01|대한수학회지 (Journal of the KMS)|제46권 제1호|pp. 31-39

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참고문헌

키워드

bifurcationgeneralized Laplacianunbounded component
주제분류수학

초록

A bifurcation problem for nonlinear partial differential equations of the form div(φ│▽u│)▽u + μ0φ(│u│)u = q(λ, x, u,▽u) subject to Dirichlet boundary conditions is discussed. Using a global bifurcation theorem of Rabinowitz type, we show that under certain conditions on φ and q, the above equation has an unbounded connected set of solutions (u,λ).

Abstract

A bifurcation problem for nonlinear partial differential equations of the form div(φ│▽u│)▽u + μ0φ(│u│)u = q(λ, x, u,▽u) subject to Dirichlet boundary conditions is discussed. Using a global bifurcation theorem of Rabinowitz type, we show that under certain conditions on φ and q, the above equation has an unbounded connected set of solutions (u,λ).

참고문헌 (13)

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  9. P. H. Rabinowitz, "A note on a nonlinear elliptic equation", Indiana Univ. Math. J., 22, pp.43~49 (1973)
  10. K. Schmitt, "Bifurcation problems associated with generalized Laplacians", Adv. Differential Equations, 9(7), pp.797~828 (2004)
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