Advances in Differential Equations

Bifurcation problems associated with generalized Laplacians

Klaus Schmitt and Inbo Sim

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This paper is concerned with bifurcation problems for nonlinear partial differential equations of the form $$-\mbox{div}(a(|\nabla u|)\nabla u) = \lambda g(u)$$ which are subject to Dirichlet boundary conditions. We show the existence of infinitely many nontrivial solutions of the eigenvalue problems in the case where $a(|t|) = |t|^{p-2}$ and $g(t) = |t|^{p-2}t, $ $p> 1.$ More general situations are also considered.

Article information

Adv. Differential Equations, Volume 9, Number 7-8 (2004), 797-828.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B32: Bifurcation [See also 37Gxx, 37K50] 35B45: A priori estimates 35B65: Smoothness and regularity of solutions 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]


Schmitt, Klaus; Sim, Inbo. Bifurcation problems associated with generalized Laplacians. Adv. Differential Equations 9 (2004), no. 7-8, 797--828.

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