Open AccessEXISTENCE OF POSITIVE SOLUTION OF TWO-POINT BOUNDARY PROBLEM FOR ONE NONLINEAR ODE OF THE FOURTH ORDER
Author(s) -
Э И Абдурагимов
Publication year - 2014
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2014-20-10-9-16
Subject(s) - mathematics , ode , nonlinear system , fixed point theorem , mathematical analysis , space (punctuation) , boundary value problem , banach space , class (philosophy) , order (exchange) , zero (linguistics) , a priori and a posteriori , boundary (topology) , point (geometry) , derivative (finance) , pure mathematics , geometry , physics , computer science , linguistics , philosophy , finance , epistemology , quantum mechanics , artificial intelligence , financial economics , economics , operating system
In the work sucient conditions for existence at least one positive solution of two-point boundary problem for one class of strongly nonlinear dierential 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 sucient 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.