一类二阶积-微分方程边值问题解的存在性与唯一性

Abstract

Abstract: By using Leray-Schauder fixed-point theorem, we discuss the existence and uniqueness of solutions for the boundary value problems of nonlinear second-order integro-differential equation, where f: ［0,1］×R²→R is continuous, S is a Fredholm type integral operator. Under proper inequality conditions of the nonlinear term f(t,x,y), the existence and uniqueness of solutions of the problem are obtained, and the results are applied to bending elastic beam equation.

Key words: integro-differential equation, boundary value problem, existence and uniqueness, fixed-point theorem, elastic beam equation

CLC Number:

O175.8

WANG Tingting, LI Yongxiang. Existence and Uniqueness of Solutions for Boundary Value Problem of a Class of Second-Order Integro-Differential Equations[J].Journal of Jilin University Science Edition, 2022, 60(5): 1036-1042.

[1]	KANG Huijun. Existence of Solutions for Periodic Problems of a Class of Second-Order Iterative Differential Equations [J]. Journal of Jilin University Science Edition, 2022, 60(5): 1043-1049.
[2]	ZHANG Cailing. Existence of Positive Solutions for Boundary Value Problems of a Class of Singular Fractional Differential Equations [J]. Journal of Jilin University Science Edition, 2022, 60(3): 487-493.
[3]	LI Xiaoping. Existence of Solutions for a Class of Caputo Fractional Derivative Boundary Value Problems with p-Laplace Operators [J]. Journal of Jilin University Science Edition, 2022, 60(3): 507-513.
[4]	KANG Huijun. Existence and Uniqueness of Solutions for a Class of Second-Order Differential Systems [J]. Journal of Jilin University Science Edition, 2022, 60(1): 20-0026.
[5]	SHANG Shuyan. Existence of Positive Solutions for Fractional Differential Equations with Infinite Multipoint Boundary Value Problems [J]. Journal of Jilin University Science Edition, 2021, 59(6): 1310-1316.
[6]	LIU Dongdong, YU Kangning, GUO Lihui. Initial Boundary Value Problem of Simplified Chromatography Equations with Riemannian Initial Value [J]. Journal of Jilin University Science Edition, 2021, 59(6): 1333-1344.
[7]	GUO Yingjia, XU Xiaorui, LI Xiaolan. Stochastic SIQR Epidemic Model with Nonmonotonic Incidence Rate Driven by Lévy Noise [J]. Journal of Jilin University Science Edition, 2021, 59(6): 1411-1418.
[8]	TANG Ying, LI Yongxiang. Existence and Uniqueness of Radial Solutions to Elliptic Boundary Value Problem with Gradient Terms on the Unit Ball [J]. Journal of Jilin University Science Edition, 2021, 59(5): 1009-1014.
[9]	YANG Wei. Existence of Infinite Positive Periodic Solutions for Nonlinear Systems with Parameters [J]. Journal of Jilin University Science Edition, 2021, 59(5): 1025-1030.
[10]	JIANG Weihua, DONG Qian. Existence of Solutions for Three-Point Boundary Value Problems of Conformable Fractional Differential Equations at Resonance [J]. Journal of Jilin University Science Edition, 2021, 59(4): 821-827.
[11]	SUN Wenchao, SU Youhui, SUN Ai. Existence and Simulation of Solutions for a Class of Nonlinear Fractional Integro-Differential Equations [J]. Journal of Jilin University Science Edition, 2021, 59(4): 828-836.
[12]	WU Ruofei. Existence and Multiplicity of Positive Solutions for Singular Third-Order Three-Point Boundary Value Problem [J]. Journal of Jilin University Science Edition, 2021, 59(4): 816-820.
[13]	WANG Rui, LU Yanqiong. Existence of Positive Solutions for a Class of Semi-positone Second-Order Discrete Periodic Boundary Value Problem with Parameter [J]. Journal of Jilin University Science Edition, 2021, 59(4): 725-730.
[14]	SHANG Shuyan, HAN Xiaoling. Existence of Positive Solutions for Integral Boundary Value Problems of Fractional Differential Equations [J]. Journal of Jilin University Science Edition, 2021, 59(3): 444-450.
[15]	FU Tongtong, LI Yongxiang. Existence of Positive Radial Solutions for Elliptic Boundary Value Problems with Gradient Terms [J]. Journal of Jilin University Science Edition, 2021, 59(3): 435-443.

Existence and Uniqueness of Solutions for Boundary Value Problem of a Class of Second-Order Integro-Differential Equations

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0