A note on bounded solutions of second order differential equations at resonance
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Differential equations, resonance, boundedness, unbounded domainAbstrakt
In the paper we study the existence of bounded solutions for differential equations of the form: $ x''-Ax= f(t,x)$, where $A\in L(H)$, $f: {\mathbb R}\times H \to H$ ($H$ -- a Hilbert space) is a continuous mapping. Using a perturbation of the equation, the Leray-Schauder topological degree and fixed point theory, we overcome the difficulty that the linear problem is non-Fredholm in any resonable Banach space.Pobrania
Opublikowane
1999-12-01
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KARPIŃSKA, Wioletta. A note on bounded solutions of second order differential equations at resonance. Topological Methods in Nonlinear Analysis [online]. 1 grudzień 1999, T. 14, nr 2, s. 371–384. [udostępniono 22.7.2024].
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