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

Li, Yan Yan

J. Differ. Equations 83, No. 2, 348-367 (1990).

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)

MSC:

35J65

Nonlinear boundary value problems for linear elliptic equations

Keywords:

nonradial positive solutions; different group actions; critical points

Citations:

Zbl 0569.35033

References:

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