References
Toland, J. F.: Global bifurcation for Neumann problems without eigenvalues J. Differential Equations44, 82–110 (1982)
Toland, J. F.: Positive solutions of nonlinear elliptic equations, existence and non-existence of solutions with radial symmetry inL p(ℝN) (preprint)
Amick, C. J., Toland, J. F.: Nonlinear elliptic eigenvalue problems on an infinite strip, global theory of bifurcation and asymptotic bifurcation (preprint)
Nehari, Z.: On a class of nonlinear integral equations. Math. Z.72, 175–183 (1959)
Agmon, S.: TheL approach to the Dirichlet problem. Ann. Scuola Norm. Sup. Pisa13, 405–448 (1959)
Gidas, B., Spruck, J.: A priori bounds for positive solutions of nonlinear elliptic equations. Comm. Pure Appl. Math.34, 525–598 (1981)
Stuart, C. A.: Bifurcation for Dirichlet problems without eigenvalues. Proc. London Math. Soc.45, 169–192 (1982)
Stuart, C. A.: Bifurcation from the essential spectrum. Proc. of Equadiff 82. In: Lecture Notes in Mathematics. Berlin, Heidelberg, New York: Springer (to appear)
Berestycki, H., Lions, P. L.: Nonlinear scalar field equations I (Existence of a ground state) and II (Existence of infinitely many solutions). Arch. Rational Mech. Anal. (to appear)
Pólya, G., Szegö, G.: Isoperimetric inequalities in mathematical physics. Princeton: Princeton University Press 1951
Bandle, C.: Isoperimetric inequalities and applications. London: Pitman 1980
Berger, M.: Nonlinearity and functional analysis. New York: Academic Press 1977
Lions, P. L.: Minimisation problems in 58-2. J. Functional Analysis41, 236–275 (1981)
Brascamp, H. J., Lieb, E. H., Luttinger, J. M.: A general rearrangement inequality for multiple integrals. J. Functional Analysis17, 227–237 (1974)
Lieb, E. H.: Existence and uniqueness of minimising solutions of Choquard's nonlinear equation. Stud. Appl. Math.57, 93–105 (1977)
Berger, M. S., Fraenkel, L. E.: A global theory of steady vortex rings in an ideal fluid. Acta Math.132, 13–51 (1974)
Coffman, C.V.: A minimum-maximum principle for a class of nonlinear integral equations. J. Analyse Math.22, 391–419 (1969)
Hempel, J.A.: Superlinear variational boundary value problems and non-uniqueness. Ph.D. thesis, University of New England, 1970
Brown, K.J.: Some operator equations with an infinite number of solutions. Quart. J. Math. Oxford25, 195–212 (1974)
Lions, P.L.: Principe de concentration-compacité en calcul des variations. C.R. Acad. Sci. Paris294, 261–264 (1982)
Lions, P.L.: Symetrie et compacité dans les espaces de Sobolev. J. Functional Analysis (to appear)
Bona, J.L., Bose, D.K., Turner, R.E.L.: Finite amplitude steady waves in stratified fluids, M.R.C. report No. 2401, July 1982.
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Stuart, C.A. A variational approach to bifurcation inL p on an unbounded symmetrical domain. Math. Ann. 263, 51–59 (1983). https://doi.org/10.1007/BF01457083
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DOI: https://doi.org/10.1007/BF01457083