ON THE NUMBER OF SOLUTIONS FOR A CERTAIN CLASS OF NONLINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEMS

A. Kirichuka; F. Sadyrbaev

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ON THE NUMBER OF SOLUTIONS FOR A CERTAIN CLASS OF NONLINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEMS

机译：关于某类非线性二阶边值问题的解决方案数量

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摘要

The boundary-value problem for the differential equation with quadratic nonlinearity x'' = âˆ’ax + bx2 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.

机译：考虑具有二次非线性X''=Â'ax+ Bx2的差分方程的边值问题x'（0）= x'（t）= 0。找到了边值问题的解决方案数。提出了说明性示例。

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来源
《Journal of Mathematical Sciences》 |2021年第1期|31-40|共10页
作者
A. Kirichuka; F. Sadyrbaev;
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作者单位

Daugavpils University;

Institute of Mathematics and Computer Science University of Latvia;

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正文语种 eng
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关键词
boundary-value problem; quadratic nonlinearity; phase trajectory; multiplicity of solutions; Jacobian elliptic function; 34B15; 34C10; 34C37;

机译：边值问题;二次非线性;相位轨迹;多种解决方案;雅各比椭圆函数;34B15;34C10;34C37;

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2. EXISTENCE AND MULTIPLICITY OF SOLUTIONS TO BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS [J] . Caixia Guo, Jianmin Guo, Shugui Kang 微分方程年刊：英文版 . 2014,第002期
3. Numerical Solutions of a Class of Nonlinear Evolution Equations with Nonlinear Term of Any Order [J] . AN Hong-Li, CHEN Yong 理论物理通讯：英文版 . 2008,第003期
4. A priori estimates for the solution of the first boundary-value problem for a class of second-order parabolic systems [J] . L. I. Kamynin, B. N. Khimchenko Izvestiya. Mathematics . 2001,第4期

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6. Existence and Multiplicity of Fast Homoclinic Solutions for a Class of Nonlinear Second-Order Nonautonomous Systems in a Weighted Sobolev Space [J] . QiongfenZhang, YuanLi Journal of Function Spaces . 2015,第1期

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7. Existence of Periodic Solutions for a Class of Second-order Nonlinear Difference Systems [C] . Tan Weiming, Sufang International conference on mechanical engineering, materials and energy . 2012

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8. Global behavior of solutions to a class of second-order rational difference equations. [D] . Basu, Sukanya. 2009

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9. Optical Diffraction in Close Proximity to Plane Apertures. I. Boundary-Value Solutions for Circular Apertures and Slits [O] . Klaus D. Mielenz 2002

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10. Unique solutions of systems of second-order nonlinear two-point boundary-value problems [O] . Manicke Robert L. 1984

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11. Positive Eigenfunctions for a Class of Second-Order Elliptic Equations with Strong Nonlinearity. [R] . clement, philippe 1976

机译：一类具有强非线性的二阶椭圆方程的正特征函数。

ON THE NUMBER OF SOLUTIONS FOR A CERTAIN CLASS OF NONLINEAR SECOND-ORDER BOUNDARY-VALUE PROBLEMS

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