Existence for Nonlinear Fourth-Order Two-Point Boundary Value Problems

被引：1

作者：

Agarwal, Ravi ^{[1
]}

Mihaylova, Gabriela ^{[2
]}

Kelevedjiev, Petio ^{[3
]}

机构：

[1] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX 78363 USA

[2] Tech Univ Sofia, Fac Engn & Pedag Sliven, Dept Elect Engn Elect & Automat, Sliven 8800, Bulgaria

[3] Tech Univ Sofia, Dept Qualificat & Profess Dev Teachers Sliven, Sliven 8800, Bulgaria

来源：

DYNAMICS | 2023年 / 3卷 / 01期

关键词：

nonlinear differential equation; fourth-order; two-point boundary conditions; solvability; barrier strips; POSITIVE SOLUTIONS; MULTIPLE SOLUTIONS; SOLVABILITY; EQUATIONS; 4TH;

D O I：

10.3390/dynamics3010010

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The present paper is devoted to the solvability of various two-point boundary value problems for the equation y(4)=f(t,y,y ',y '',y & tprime;), where the nonlinearity f may be defined on a bounded set and is needed to be continuous on a suitable subset of its domain. The established existence results guarantee not just a solution to the considered boundary value problems but also guarantee the existence of monotone solutions with suitable signs and curvature. The obtained results rely on a basic existence theorem, which is a variant of a theorem due to A. Granas, R. Guenther and J. Lee. The a priori bounds necessary for the application of the basic theorem are provided by the barrier strip technique. The existence results are illustrated with examples.

引用

页码：152 / 170

页数：19

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