On the Number of Solutions for a Certain Class of Nonlinear Second-Order Boundary-Value Problems

The boundary-value problem for the differential equation with quadratic nonlinearity x'' = −ax + bx 2 with the boundary conditions x' (0) = x' ( T ) = 0 is considered. The number of solutions of the boundary-value problem is found. An illustrative example is presented.

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 257; no. 1; pp. 31 - 40
Main Authors Kirichuka, A., Sadyrbaev, F.
Format Journal Article
LanguageEnglish
Published New York Springer US 04.08.2021
Springer
Springer Nature B.V
Subjects
Boundary conditions
Boundary value problems
Differential equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Quadratic equations
34C37
34B15
multiplicity of solutions
34C10
Jacobian elliptic function
phase trajectory
boundary-value problem
quadratic nonlinearity
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Summary:The boundary-value problem for the differential equation with quadratic nonlinearity x'' = −ax + bx 2 with the boundary conditions x' (0) = x' ( T ) = 0 is considered. The number of solutions of the boundary-value problem is found. An illustrative example is presented.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05467-3