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A Survey of Nonlinear Sturm-Liouville Equations

In: Sturm-Liouville Theory

Author

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  • Chao-Nien Chen

    (National Changhua University of Education, Department of Mathematics)

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.

Suggested Citation

  • Chao-Nien Chen, 2005. "A Survey of Nonlinear Sturm-Liouville Equations," Springer Books, in: Werner O. Amrein & Andreas M. Hinz & David P. Pearson (ed.), Sturm-Liouville Theory, pages 201-216, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7359-7_9
    DOI: 10.1007/3-7643-7359-8_9
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