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The aim of this paper is to explore the method of lower and upper solutions in order to give some existence results for equations of the form $$y^{(4)}(x)+(k_{1}+k_{2}) yu0027u0027(x)+k_{1}k_{2} y(x)=fbigl(x,y(x)bigr), quad xin(0,1), $$with the Navier condition $$y(0) = y(1) = yu0027u0027(0) = yu0027u0027(1) = 0 $$under the condition (k_{1}u003c0u003ck_{2}u003cpi^{2}). The main tool is the Schauder fixed point theorem.

The method of lower and upper solutions for fourth order equations with the Navier condition