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Multiplicity Results for Boundary Value Problems with Potentials Oscillating around Resonance

✍ Scribed by Patrick Habets; Enrico Serra; Massimo Tarallo

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
440 KB
Volume
138
Category
Article
ISSN
0022-0396

No coin nor oath required. For personal study only.

✦ Synopsis

Consider the Dirichlet boundary value problem

) u=0, on 0, where 0 is a bounded domain R N and * 1 is the first eigenvalue of &2 in 0, under Dirichlet boundary conditions. Let . 1 be the corresponding eigenfunction. Such a resonance problem is easy to deal with if the potential G(x, u)= | u 0 g(x, s) ds satisfies the condition lim |a| Γ„ +

| 0 G(x, a. 1 (x)) dx=& .

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