Existence of many positive solutions of semilinear equations on annulus. (English) Zbl 0748.35013

Der Autor zeigt: Die Anzahl der positiven nichtäquivalenten nichtrotationssymmetrischen Lösungen von \(-\Delta u-u^ p=0\) in Ringgebieten unter Dirichlet Nullrandbedingungen strebt gegen \(\infty\), wenn der äußere Kugelradius gegen \(\infty\) geht. Ringgebiete zeigen somit ein deutlich anderes Verhalten als die Kugel.
Reviewer: J.Frehse (Bonn)


35J65 Nonlinear boundary value problems for linear elliptic equations


Zbl 0569.35033
Full Text: DOI


[1] Brezis, H.; Nirenberg, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure. Appl. Math., 36, 437-477 (1983) · Zbl 0541.35029
[2] Cerami, G.; Solimini, S.; Struwe, M., Some existence results for superlinear elliptic boundary value problems involving critical exponents, J. Funct. Anal., 69, 289-306 (1986) · Zbl 0614.35035
[3] Coffman, C. V., A nonlinear boundary value problem with many positive solutions, J. Differential Equations, 54, 429-437 (1984) · Zbl 0569.35033
[5] Ding, Wei-Yue; Ni, Wei-Ming, On the existence of positive entire solutions of a semi-linear elliptic equation, Arch. Rational Mech. Anal., 91, 288-308 (1986) · Zbl 0616.35029
[6] Gidas, B.; Ni, W.; Nirenberg, L., Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68, 209-243 (1979) · Zbl 0425.35020
[7] Gilbarg, D.; Trudinger, N. S., Elliptic Partial Differential Equations, (Grundlehren der mathematischen Wissenschaften 224 (1983), Springer-Verlag: Springer-Verlag Berlin/Heidelberg) · Zbl 0691.35001
[10] Rabinowitz, P. H., Variational Methods for Nonlinear Eigenvalue Problems, ((1974), Edicioni Cremonese: Edicioni Cremonese Roma), 141-195
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.