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Multiplicity results for problems with uniform norms in boundary conditions

✍ Scribed by S.A. Brykalov

Book ID
104331149
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
573 KB
Volume
30
Category
Article
ISSN
0362-546X

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✦ Synopsis

Method of monotone boundary conditions, nonlinear functional boundary conditions, Co-norms in boundary conditions, nonlinear boundary value problems for ordinary differential and functional differential equations; existence, nonuniqueness, and the number of solutions.

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## 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

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## Abstract Let us consider the boundary‐value problem equation image where __g__: ℝ β†’ ℝ is a continuous and __T__ ‐periodic function with zero mean value, not identically zero, (__Ξ»__, __a__) ∈ ℝ^2^ and $ \tilde h $ ∈ __C__ [0, __Ο€__ ] with ∫^__Ο€__^ ~0~ $ \tilde h $(__x__) sin __x dx__ = 0. If _