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In this paper, the behaviour of the positive eigenfunction of in u| = 0, p > 1, isstudied near its critical points. Under some convexity and symmetryassumptions on , is seen to have a unique critical point atx = 0; also, the behaviour of both and is determined nearby.Positive solutions u to some general problems pu = f(u)in , u| = 0, are also considered, with some convexity restrictionson u. 2000 Mathematics Subject Classification 35B05 (primary),35J65, 35J70 (secondary). 相似文献
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A bifurcation problem governed by the boundary condition II 总被引:1,自引:0,他引:1
Garcia-Melian Jorge; Rossi Julio D.; Sabina De Lis Jose C. 《Proceedings London Mathematical Society》2007,94(1):1-25
In this work we consider the problem u = a(x)up in on , where is a smooth bounded domain, isthe outward unit normal to , is regarded as a parameter and0 < p < 1. We consider both cases where a(x) > 0 in or a(x) is allowed to vanish in a whole subdomain 0 of . Ourmain results include existence of non-negative non-trivial solutionsin the range 0 < < 1, where 1 is characterized by meansof an eigenvalue problem, uniqueness and bifurcation from infinityof such solutions for small , and the appearance of dead coresfor large enough . 相似文献
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