## Topological Methods in Nonlinear Analysis

### A note on bounded solutions of second order differential equations at resonance

Wioletta Karpińska

#### Abstract

In the paper we study the existence of bounded solutions for differential equations of the form: $x''-Ax= f(t,x)$, where $A\in L(H)$, $f\colon {\mathbb R}\times H \to H$ ($H$ - 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 14, Number 2 (1999), 371-384.

Dates
First available in Project Euclid: 29 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1475179851

Mathematical Reviews number (MathSciNet)
MR1766179

Zentralblatt MATH identifier
0960.34042

#### Citation

Karpińska, Wioletta. A note on bounded solutions of second order differential equations at resonance. Topol. Methods Nonlinear Anal. 14 (1999), no. 2, 371--384. https://projecteuclid.org/euclid.tmna/1475179851

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