Publication Date:
2014-11-24
Description:
In this paper, we investigate the solvability of nth-order Lipschitz equations y ( n ) = f ( x , y , y ′ , … , y ( n − 1 ) ) , x 1 ≤ x ≤ x 3 , with nonlinear three-point boundary conditions of the form k ( y ( x 2 ) , y ′ ( x 2 ) , … , y ( n − 1 ) ( x 2 ) ; y ( x 1 ) , y ′ ( x 1 ) , … , y ( n − 1 ) ( x 1 ) ) = 0 , g i ( y ( i ) ( x 2 ) , y ( i + 1 ) ( x 2 ) , … , y ( n − 1 ) ( x 2 ) ) = 0 , i = 0 , 1 , … , n − 3 , h ( y ( x 2 ) , y ′ ( x 2 ) , … , y ( n − 1 ) ( x 2 ) ; y ( x 3 ) , y ′ ( x 3 ) , … , y ( n − 1 ) ( x 3 ) ) = 0 , where n ≥ 3 , x 1 〈 x 2 〈 x 3 . By using the matching technique together with set-valued function theory, the existence and uniqueness of solutions for the problems are obtained. Meanwhile, as an application of our results, an example is given.MSC:34B10, 34B15.
Print ISSN:
1687-2762
Electronic ISSN:
1687-2770
Topics:
Mathematics
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