References
Brezis, H., Nirenberg, L.: Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure App. Math.36, 437–444 (1983)
Cafarelli, L.A., Gidas, B., Spruck, J.: Asymptotic symmetry and local behaviour of semilinear elliptic equations with Sobolev exponent. Comm. Pure App. Math.42, 271–297 (1989)
Coffman, C.V.: A nonlinear boundary value problem with many positive solutions. J. Diff. Equations54, 429–437 (1984)
Dancer, E.N.: The effect of domain shape on the number of positive solutions of certain nonlinear equations. J. Diff. Equations74, 120–156 (1988)
Dancer, E.N.: On the influence of domain shape on the existence of large solutions of some superlinear problems. Math. Ann.285, 647–669 (1990)
Dancer, E.N.: A note on an equation with critical exponent. Bull. Lond. Math. Soc.20, 600–602 (1988)
Dancer, E.N.: Certain weakly nonlinear partial differential equations on annuli. Nonlinear Anal.14, 441–442 (1990)
Dancer, E.N.: A new degree forS 1-invariant gradient mappings and applications. Analyse Nonlineaire2, 329–370 (1985)
Figueredo, de, D.G., Lions, P.L., Nussbaum, R.: A priori estimates and existence of positive solutions of semilinear elliptic equations. J. Math. Pure et Appliquées61, 41–63 (1982)
Gidas, B., Ni, W., Nirenberg, L.: Symmetry and related properties by the maximum principle. Commun. Math. Phys.68, 209–243 (1979)
Gidas, B., Spruck, J.: Global and local behaviour of positive solutions of nonlinear elliptic equations. Commun. Pure Appl. Math.34, 525–598 (1981)
Gidas, B., Spruck, J.: A priori bounds for positive solutions of nonlinear elliptic equations. Commun. Partial Differ. Equations6, 883–901 (1981)
Gilbarg, D., Trudinger, N.: Elliptic partial differential equations of second order. Berlin Heidelberg New York: Springer 1977
Li, Yan Yan: Existence of many positive solutions of semilinear elliptic equations on annulus. J. Differ. Equations83, 348–367 (1990)
Lin, S.S.: On non radially symmetric bifurcation in the annulus. J. Differ. Equations80, 251–279 (1989)
Ni, W., Nussbaum, R.: Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r)=0. Commun. Pure Appl. Math.38, 67–108 (1985)
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Dancer, E.N. On the number of positive solutions of some weakly nonlinear equations on annular regions. Math Z 206, 551–562 (1991). https://doi.org/10.1007/BF02571362
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DOI: https://doi.org/10.1007/BF02571362