6533b862fe1ef96bd12c606f
RESEARCH PRODUCT
Types of solutions and multiplicity results for two-point nonlinear boundary value problems
Felix SadyrbaevInara Yermachenkosubject
Nonlinear systemApplied MathematicsMathematical analysisFree boundary problemPoint (geometry)Mixed boundary conditionBoundary value problemType (model theory)AnalysisElliptic boundary value problemDomain (mathematical analysis)Mathematicsdescription
Abstract Two-point boundary value problems for the second-order ordinary nonlinear differential equations are considered. If the respective nonlinear equation can be reduced to a quasi-linear one with a non-resonant linear part and both equations are equivalent in some domain D , and if solutions of the quasi-linear problem lie in D , then the original problem has a solution. We then say that the original problem allows for quasilinearization. We show that a quasi-linear problem has a solution of definite type which corresponds to the type of the linear part. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-11-01 | Nonlinear Analysis: Theory, Methods & Applications |