Geodesic
Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity
Canadian journal of mathematics, Tome 49 (1997) no. 5, pp. 1066-1088

Voir la notice de l'article provenant de la source Cambridge University Press

We consider the multiparameter nonlinear Sturm-Liouville problem where are parameters. We assume that1 ≤ q ≤ p1 < p2 < ... ≤ pn < 2q + 3.We shall establish an asymptotic formula of variational eigenvalue λ = λ(μ, α) obtained by using Ljusternik-Schnirelman theory on general level set Nμ, α (α < 0 : parameter of level set). Furthermore,we shall give the optimal condition of {(μ, α)}, under which μi (m + 1 ≤ i ≤ n : fixed) dominates the asymptotic behavior of λ(μ, α).
DOI : 10.4153/CJM-1997-053-0
Mots-clés : 34B15, 34B25 
Shibata, Tetsutaro. Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity. Canadian journal of mathematics, Tome 49 (1997) no. 5, pp. 1066-1088. doi: 10.4153/CJM-1997-053-0
@article{10_4153_CJM_1997_053_0,
     author = {Shibata, Tetsutaro},
     title = {Multiparameter {Variational} {Eigenvalue} {Problems} {With} {Indefinite} {Nonlinearity}},
     journal = {Canadian journal of mathematics},
     pages = {1066--1088},
     year = {1997},
     volume = {49},
     number = {5},
     doi = {10.4153/CJM-1997-053-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-053-0/}
}
TY  - JOUR
AU  - Shibata, Tetsutaro
TI  - Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity
JO  - Canadian journal of mathematics
PY  - 1997
SP  - 1066
EP  - 1088
VL  - 49
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-053-0/
DO  - 10.4153/CJM-1997-053-0
ID  - 10_4153_CJM_1997_053_0
ER  - 
%0 Journal Article
%A Shibata, Tetsutaro
%T Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity
%J Canadian journal of mathematics
%D 1997
%P 1066-1088
%V 49
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-053-0/
%R 10.4153/CJM-1997-053-0
%F 10_4153_CJM_1997_053_0

[1] 1. Berestycki, H. and Lions, P.L., Nonlinear scalar field equations, I, Existence of a ground state, Arch. Rational Mech. Analysis 82(1983), 313–345. Google Scholar

[2] 2. Faierman, M., Two-parameter eigenvalue problems in ordinary differential equations, Longman House, Essex, UK. Google Scholar

[3] 3. Gidas, B.,Ni, W.M. and L.Nirenberg, Symmetry and related properties via the maximum principle, Commn. Math. Phys. 68(1979), 209–243. Google Scholar

[4] 4. Shibata, T., Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems, J. Analyse Math. 66(1995), 277–294. Google Scholar

[5] 5. Shibata, T., Variational eigencurve and bifurcation for two-parameter nonlinear Sturm-Liouville equations, Topol. Methods Nonlinear Anal. 8(1996. 79–93. Google Scholar

[6] 6. Turyn, L., Sturm-Liouville problems with several parameters, J. Differential Equations 38(1980), 239–259. Google Scholar

[7] 7. Zeidler, E., Ljusternik-Schnirelman theory on general level sets, Math. Nachr. 129(1986), 235–259. Google Scholar

Cité par Sources :