This paper is devoted to the study the nonlinear boundary value problem . We state a maximum principle related with the operator and apply it to prove the existence and approximation of solutions to the problem (i), (ii), in presence of properly ordered lower and upper functions.
Yermachenko, I. (2011). Maximum principle and the fourth order boundary value problem. Mathematical Modelling and Analysis, 16(1), 143-152. https://doi.org/10.3846/13926292.2011.562931
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. We state a maximum principle related with the operator 
and apply it to prove the existence and approximation of solutions to the problem (i), (ii), in presence of properly ordered lower and upper functions.