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The method of lower and upper solutions for second, third, fourth, and higher order boundary value problems. (English) Zbl 0807.34023
The problem u (n) =f(t,u), t[a,b], u (i) (a)=u (i) (b)=λ i , i=0,1,,n-1 is solved by means of the monotone iterative method. The best estimates for the constant M in the statement u (n) +Mu0, M>0 (M<0), u (i) (a)=u (i) (b), i=0,1,,n-1 imply that u0 in [a,b] (u0 in [a,b]) are contained for n=2, M>0, n=3, M0, n=4, M<0 and for n=2k6 the known estimate for M<0 is improved.
MSC:
34B15Nonlinear boundary value problems for ODE