Krasnosel'skii, A. M. and Kuznetsov, N. A. and Rachinskii, D. I. (2002) On resonant differential equations with unbounded non-linearities. ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 21 (3). pp. 639-668. ISSN 0232-2064
Full text not available from this repository. (Request a copy)Abstract
We present a method to study asymptotically linear degenerate problems with sublinear unbounded non-lineari ties. The method is based on the uniform convergence to zero of projections of non-linearity increments onto some finite-dimensional spaces. Such convergence was used for the analysis of resonant equations with bounded non-linearities by many authors. The unboundedness of nonlinear terms complicates essentially the analysis of most problems: existence results, approximate methods, systems with parameters, stability, dissipativity, etc. In this paper we present statements on projection convergence for unbounded non-linearities and apply them to various resonant asymptotically linear problems: existence of forced periodic oscillations and unbounded sequences of such oscillations, existence of unbounded solutions, sharp analysis of integral equations with simple degeneration of the linear part (a scalar two-point boundary value problem is considered as an example), existence of non-trivial cycles for higher order autonomous ordinary differential equations, and Hopf bifurcations at infinity.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | OSCILLATING NONLINEARITIES; CONTROL-SYSTEMS; VECTOR-FIELDS; EXISTENCE; non-linearity sublinear at infinity; degenerate linear parts; periodic solutions; cycles; integral equations; two-point problems; Hopf bifurcation; existence results |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Nov 2021 08:11 |
| Last Modified: | 22 Nov 2021 08:11 |
| URI: | https://pred.uni-regensburg.de/id/eprint/40850 |
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