Existence and properties of solutions for boundary value problems based on the nonlinear reactor dynamics
| Autor: | Aleksandra Orpel |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Class (set theory) Pure mathematics Applied Mathematics 010102 general mathematics Dynamics (mechanics) 02 engineering and technology General Chemistry Fixed point 021001 nanoscience & nanotechnology 01 natural sciences Prime (order theory) Nonlinear system Boundary value problem Uniqueness 0101 mathematics 0210 nano-technology Variable (mathematics) |
| Zdroj: | Journal of Mathematical Chemistry. 58:1420-1436 |
| ISSN: | 1572-8897 0259-9791 |
| DOI: | 10.1007/s10910-020-01134-1 |
| Popis: | We deal with the existence of positive solutions for the following class of nonlinear equation $$u^{\prime \prime }(t)+Au^{\prime }(t)+g(t,u(t),v(t))=0$$ u ″ ( t ) + A u ′ ( t ) + g ( t , u ( t ) , v ( t ) ) = 0 a.e. in (0, 1), with boundary conditions $$u^{\prime }(0)=0$$ u ′ ( 0 ) = 0 , $$u^{\prime }(1)+Au(1)=0$$ u ′ ( 1 ) + A u ( 1 ) = 0 , where v is a functional parameter. The form of the problem is associated with the classical model described by Markus and Amundson. We show the existence of at least one positive solution of this problem and discuss its properties. Moreover we describe conditions that guarantee the continuous dependence of solution on parameter v also in the case of the lack of the uniqueness of a solution. The results are based on the clasical fixed point methods. Our approach allows us to consider both sub and superlinear nonlinearities which may be singular with respect to the first variable. |
| Databáze: | OpenAIRE |
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