A Survey of Nonlinear Sturm-Liouville Equations

Chao-Nien Chen ()
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Chao-Nien Chen: National Changhua University of Education, Department of Mathematics

A chapter in Sturm-Liouville Theory, 2005, pp 201-216 from Springer

Abstract: Abstract This note gives a brief survey of existence, uniqueness and bifurcation results for nonlinear Sturm-Liouville equations. Early in 1960, Nehari made an interesting proposal to study solutions with a prescribed number of nodes. His ideas have had a great influence on critical point theory as a branch of the calculus of variations. Rabinowitz established a global bifurcation theorem based on the nodal properties of solutions. Some results on bifurcation from the lowest point of the continuous spectrum will also be discussed.

Date: 2005
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DOI: 10.1007/3-7643-7359-8_9

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