The effect of variational framework on the spectral asymptotics for nonlinear elliptic two-parameter problems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1999)
- Volume: 28, Issue: 3, page 545-567
- ISSN: 0391-173X
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topShibata, Tetsutaro. "The effect of variational framework on the spectral asymptotics for nonlinear elliptic two-parameter problems." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 28.3 (1999): 545-567. <http://eudml.org/doc/84387>.
@article{Shibata1999,
author = {Shibata, Tetsutaro},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {two-parameter eigenvalue problems; variational problems; Lagrange multipliers; asymptotic expansion},
language = {eng},
number = {3},
pages = {545-567},
publisher = {Scuola normale superiore},
title = {The effect of variational framework on the spectral asymptotics for nonlinear elliptic two-parameter problems},
url = {http://eudml.org/doc/84387},
volume = {28},
year = {1999},
}
TY - JOUR
AU - Shibata, Tetsutaro
TI - The effect of variational framework on the spectral asymptotics for nonlinear elliptic two-parameter problems
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1999
PB - Scuola normale superiore
VL - 28
IS - 3
SP - 545
EP - 567
LA - eng
KW - two-parameter eigenvalue problems; variational problems; Lagrange multipliers; asymptotic expansion
UR - http://eudml.org/doc/84387
ER -
References
top- [1] C. Bandle, "Isoperimetric Inequalities and Applications", Pitman, Boston,1980. Zbl0436.35063MR572958
- [2] H. Berestycki - P.L. Lions, Nonlinear scalar field equations, I existence of a ground state, Arch. Rat. Mech. Anal.82 (1983), 313-345. Zbl0533.35029MR695535
- [3] P. Binding - P.J. Browne, Asymptotics of eigencurves for second order ordinary differential equations, I, J. Differential Equations88 (1990), 30-45. Zbl0723.34073MR1079857
- [4] P. Binding - P.J. Browne, Asymptotics of eigencurves for second order ordinary differential equations, II, J. Differential Equations89 (1991), 224-243. Zbl0738.34043MR1091477
- [5] P. Binding - H. Volkmer, Eigencurves for two-parameter Sturm-Liouville equations, SIAM Rev.38 (1996), 27-48. Zbl0869.34020MR1379040
- [6] P.J. Browne - B.D. Sleeman, Nonlinear multiparameter Sturm-Liouville problems, J. Differential Equations34 (1979), 139-146. Zbl0386.34028MR549588
- [7] R. Chiappinelli, Remarks on bifurcation for elliptic operators with odd nonlinearity, Israel J. Math.65 (1989), 285-292. Zbl0678.35005MR1005012
- [8] E.N. Dancer, On the uniqueness of the positive solution of a singularly perturbed problem, Rocky Mountain J. Math.25 (1995), 957-975. Zbl0846.35046MR1357103
- [9] M. Faierman, "Two-parameter eigenvalue problems in ordinary differential equations", Longman House, Essex, UK, 1991. Zbl0755.34084MR1124402
- [10] B. Gidas - W.M. Ni - L. Nirenberg, Symmetry and related properties via the maximum principle, Commn. Math. Phys.68 (1979), 209-243. Zbl0425.35020MR544879
- [11] D. Gilberg - N.S. Trudinger, "Elliptic partial differential equations of second order", Springer, New York, 1983. Zbl0562.35001MR737190
- [12] J.L. Gómez, Multiparameter local bifurcation based on the linear part, J. Math. Anal. Appl.138 (1989), 358-370. Zbl0668.47042MR991030
- [13] M.K. Kwong, Uniqueness of positive solutions of Δu - u + up = 0 in RN, Arch. Rat. Mech. Anal.105 (1989), 243-266. Zbl0676.35032
- [14] C.S. Lin - W.M. Ni - I. Takagi, Large amplitude stationary solutions to a chemotaxis system, J. Differential Equations72 (1988), 1-27. Zbl0676.35030MR929196
- [15] W.M. Ni - I. Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math.44 (1991), 819-851. Zbl0754.35042MR1115095
- [16] W.M. Ni - J. Wei, On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math.48 (1995), 731-768. Zbl0838.35009MR1342381
- [17] B.P. Rynne, Bifurcation from eigenvalues in nonlinear multiparameter problems, Nonlinear Anal.15 (1990), 185-198. Zbl0702.47043MR1065251
- [18] B.P. Rynne, Uniform convergence of multiparameter eigenfunction expansions, J. Math. Anal. Appl.147 (1990), 340-350. Zbl0724.34088MR1050209
- [19] T. Shibata, Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems, J. Analyse Math. 66 (1995), 277-294. Zbl0844.34092MR1370353
- [20] T. Shibata, Spectral asymptotics of nonlinear elliptic multiparameter problems, (preprint). Zbl0861.35071
- [21] E. Zeidler, Ljusternik-Schnirelman theory on general level sets, Math. Nachr.129 (1986), 235-259. Zbl0608.58014MR864637
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