Geodesic
Existence and uniqueness of nontrivial solutions for nonlinear higher-order three-point eigenvalue problems on time scales
Electronic journal of differential equations, Tome 2008 (2008)
In this paper, we study a nonlinear higher-order three-point eigenvalue problems with first-order derivative on time scales. Under certain growth conditions on the nonlinearity, sufficient conditions for existence and uniqueness of nontrivial solutions, which are easily verifiable, are obtained by using the Leray-Schauder nonlinear alternative. The conditions used in the paper are different from those in [4, 10, 21]. To show applications of our main results, we present some examples.
Classification : 39A10, 34B15, 34B18
Keywords: time scale, nontrivial solutions, eigenvalue problem, fixed point theorem, Leray-Schauder nonlinear alternative 
@article{EJDE_2008__2008__a24,
     author = {Han,  Wei and Kao,  Yonggui},
     title = {Existence and uniqueness of nontrivial solutions for nonlinear higher-order three-point eigenvalue problems on time scales},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1169.39301},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a24/}
}
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Han,  Wei; Kao,  Yonggui. Existence and uniqueness of nontrivial solutions for nonlinear higher-order three-point eigenvalue problems on time scales. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a24/