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A Local Bifurcation Theorem for Degenerate Elliptic Equations With Radial Symmetry

✍ Scribed by J. Garcı́a-Melián; J. Sabina de Lis

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
173 KB
Volume
179
Category
Article
ISSN
0022-0396

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✦ Synopsis

In this work we provide local bifurcation results for equations involving the p-Laplacian in balls. We analyze the continua C n of radial solutions emanating from (l n, p , 0), {l n, p } being the radial eigenvalues of -D p . First, we show that the only nontrivial solutions close to (l n, p , 0) lie on a continuous curve, thus extending the Crandall-Rabinowitz theorem. Second, it is proved that C n 0 {(l n, p , 0)} splits into two unbounded connected pieces, characterized by their nodal properties thus sharpening previous results.

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