@article{Zhang2023, 
author = {Yanhong Zhang and Li Chen},
title = {Positive solution for a class of nonlinear fourth-order boundary value problem},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {1014-1021},
keywords = {fourth-order differential operator, positive solution, boundary value problem, Leray-Schauder's fixed point theorem},
url = {https://www.sciopen.com/article/10.3934/math.2023049},
doi = {10.3934/math.2023049},
abstract = {In this paper, we are concerned with the existence of positive solutions for boundary value problems of nonlinear fourth-order differential equations                                             u                      (            4            )                          +        c        (        x        )        u        =        λ        a        (        x        )        f        (        u        )        ,                        x        ∈        (        0        ,        1        )        ,                                        u        (        0        )        =        u        (        1        )        =                  u          ″                (        0        )        =                  u          ″                (        1        )        =        0        ,            where    a  (  x  ) may change signs. The proof of main results is based on Leray-Schauder's fixed point theorem and the properties of Green's function of the fourth-order differential operator        L    c    u  =      u          (      4      )        +  c  (  x  )  u.}
}