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We study the existence and multiplicity of positive solutions of the nonlinear fourth order problem
⎧ in (0,1),
⎨
⎩u(0) = a ≥ 0, u’(0) = a’ ≥ 0, u(1) = b ≥ 0, u(1) = -b’ ≤ 0
The methods employed are upper and lower solutions and degree theory arguments.
Estesa la cosiddetta Picone integral identity a certi operatori a derivate parziali del quart'ordine, se ne traggono teoremi di tipo sturmiano per le soluzioni di equazioni competenti a tali operatori, nonché diseguaglianze di un tipo dovuto a Wirtinger e limitazioni inferiori per gli autovalori di un parametro da cui dipendono le equazioni omogenee relative agli operatori considerati, con condizioni di nullità, alla frontiera, della soluzione e di un certo operatore su essa, lineare del second'ordine....
We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.
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