Abstract
By the theory of differential inequality, bounding function method, and the theory of topological degree, this paper presents the existence criterions of solutions for the general th-order differential equations under nonlinear boundary conditions, and extends many existing results.
Highlights
From Nagumo [10], there have been many accomplishments on the study of the existence of solutions for boundary value problems (BVPs) using the theory of differential inequality
We are concerned with the nth-order nonlinear BVP: y(n) = f t, y, y, . . . , y(n−1), Pi y(a), y (a), . . . , y(n−1)(a) = 0, i = 1, . . . , n − 1, Pn y(b), y (b), . . . , y(n−1)(b) = 0, (1.1)
By the solvability theorem of topological degree, it is clear that there exists some y(t) satisfying (2.17), this proposition is proved
Summary
From Nagumo [10], there have been many accomplishments on the study of the existence of solutions for boundary value problems (BVPs) using the theory of differential inequality (cf. [1,2,3,4,5,6,7,8,9, 11,12,13,14,15,16,17]). For the nth-order nonlinear differential equations with the nonlinear boundary conditions, results are very few. We get the new BVP which will be discussed firstly, the judgement of the existence of solutions for the original BVP will be attained naturally.
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