×

zbMATH — the first resource for mathematics

Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions. (English) Zbl 0249.35029

MSC:
35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Berger, M. S., Stationary states for a nonlinear wave equation. J. Math. Physics 11, 2906–2912 (1970). · Zbl 0201.12602
[2] Betts, D. D., H. Schiff, & W. B. Strickfaden, Approximate gnsolution of a nonlinear field equation. J. Math. Physics 4, 334–338 (1963). · Zbl 0128.46003
[3] Coffman, C. V., On the equat
[4] Coffman, C. V., Spectral theory of monotone Hammerstein operators. Pac. J. Math. 36, 303–322 (1971). · Zbl 0212.46803
[5] Coffman, C. V., A minimum-maximum principle for a class of non-linear integral equations. J. d’Analyse Math. 22, 391–419 (1969). · Zbl 0179.15601
[6] Coffman, C. V., On the positive solutions of boundary-value problems for a class of nonlinear differential equations. J. Diff. Eq. 3, 92–111 (1967). · Zbl 0152.08603
[7] Coffman, C. V., & A. J. Das, A class of eigenvalues of the fine structure constant and internal energy obtained from a class of exact solutions of the combined Klein-Gordon-Maxwell-Einstein field equations. J. Math. Physics 8, 1720–1735 (1967). · Zbl 0157.32204
[8] Conner, P. E., & E. E. Floyd, Fixed point free involutions and equivariant maps. Bull. Amer. Math. Soc. 66, 416–441 (1960). · Zbl 0106.16301
[9] Dugundji, J., Topology. Boston: Allyn and Bacon 1966.
[10] Finklestein, R., R. Lelevier, & M. Ruderman, Nonlinear spinor fields. Phys. Review 83, 326–332 (1951). · Zbl 0043.21603
[11] Friedman, A., Partial Differential Equations. New York: Holt. Rinehart and Winston (1969). · Zbl 0224.35002
[12] Hartman, P., Ordinary Differential Equations. New York: Wiley (1964). · Zbl 0125.32102
[13] Kolodner, I. I., Heavy rotating string–a nonlinear eigenvalue problem. Comm. Pure and Appl. Math. 8, 395–408 (1955). · Zbl 0065.17202
[14] Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach (1963). · Zbl 0121.42701
[15] Moser, J., A sharp form of an inequality by N. Trudinger. Indiana University Mathematics Journal 20, 1077–1092 (1971). · Zbl 0203.43701
[16] Mostow, G. D., Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms. Inst. des Hautes Études Scient., Publ. Math., No 34 (1968). · Zbl 0189.09402
[17] Nehari, Z., On a nonlinear differential equation arising in nuclear physics. Proc. Royal Irish Academy, 62, 117–135 (1963). · Zbl 0124.30204
[18] Nirenberg, L., Remarks on strongly elliptic partial differential equations, Comm. Pure and Appl. Math. 8, 648–674 (1955). · Zbl 0067.07602
[19] Pólya, G., & G. Szegö, Isoperimetric Inequalities in Mathematical Physics. Princeton: Princeton University Press (1951). · Zbl 0044.38301
[20] Robinson, P. D., Extremum pri · Zbl 0205.09901
[21] Ryder, G. H., Boundary value problems for a class of nonlinear differential equations. Pac. J. Math. 22, 477–503 (1967). · Zbl 0152.28303
[22] Synge, J. L., On a certain nonlinear differential equation. Proc. Royal Irish Academy 62, 17–42 (1961). · Zbl 0104.31501
[23] Teshima, R. K., M. Sc. Thesis. University of Alberta, Edmonton, Alberta, Canada, (1960).
[24] Weiss, S., Nonlinear eigenvalue problems. Ph. D. Dissertation, University of Chicago, August 1969.
[25] Wolkowisky, J. H., Existence of buckled states of circular plates. Comm. Pure and Appl. Math. 20, 549–560 (1967). · Zbl 0168.45206
[26] Sansone, G., Su un’equazione differenziale non lineare della fisica nucleare, Symposia Mathematica, vol. VI. Istituto Nazionale di Alta Matematica, Bologna (1970).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.