Geodesic
Lyapunov inequalities for Neumann boundary conditions at higher eigenvalues
Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 163-178.

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This paper is devoted to the study of Lyapunov-type inequality for Neumann boundary conditions at higher eigenvalues. Our main result is derived from a detailed analysis about the number and distribution of zeros of nontrivial solutions and their first derivatives, together with the use of suitable minimization problems. This method of proof allows to obtain new information on Lyapunov constants. For instance, we prove that as in the classical result by Lyapunov, the best constant is not attained. Additionally, we exploit the relation between Neumann boundary conditions and disfocality to provide new nonresonance conditions at higher eigenvalues.
DOI : 10.4171/jems/193
Classification : 34-XX, 00-XX
Keywords: Neumann boundary value problems, resonante, higher eigenvalues, Lyapunov inequalities, existente and uniqueness 
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     author = {Antonio Ca\~nada and Salvador Villegas},
     title = {Lyapunov inequalities for {Neumann} boundary conditions at higher eigenvalues},
     journal = {Journal of the European Mathematical Society},
     pages = {163--178},
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     year = {2010},
     doi = {10.4171/jems/193},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/193/}
}
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Antonio Cañada; Salvador Villegas. Lyapunov inequalities for Neumann boundary conditions at higher eigenvalues. Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 163-178. doi : 10.4171/jems/193. http://geodesic.mathdoc.fr/articles/10.4171/jems/193/

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