## 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
β¦ LIBER β¦
A Nonlinear Boundary Value Problem with Potential Oscillating Around the First Eigenvalue
β Scribed by P. Habets; R. Manasevich; F. Zanolin
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 497 KB
- Volume
- 117
- Category
- Article
- ISSN
- 0022-0396
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## Abstract Let us consider the boundaryβvalue problem equation image where __g__: β β β is a continuous and __T__ βperiodic function with zero mean value, not identically zero, (__Ξ»__, __a__) β β^2^ and $ \tilde h $ β __C__ [0, __Ο__ ] with β«^__Ο__^ ~0~ $ \tilde h $(__x__) sin __x dx__ = 0. If _