EXISTENCE OF POSITIVE SOLUTION OF TWO-POINT BOUNDARY PROBLEM FOR ONE NONLINEAR ODE OF THE FOURTH ORDER

In the work sufficient conditions for existence at least one positive solution of two-point boundary problem for one class of strongly nonlinear differential equations of the fourth order are received. The problem is considered on a segment [0,1] (more general case of segment[0, a] is reduced to considered). On the ends of a segment the solution of y and its second derivative of y′′ areequal to zero. Right part of an equation f (x, y) isn’t negative at x\geq 0 andat all y. Performance of sufficient conditions is easily checked. Performance ofthese conditions is easily checked. In the proof of existence the theory of conesin banach space is used. Also apriori estimates of positive solution, which ispossible to use further at numerical construction of the solution are obtained.

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