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Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

Lingbin Kong, Daqing Jiang (1998)

Annales Polonici Mathematici

The fourth order periodic boundary value problem u ( 4 ) - m u + F ( t , u ) = 0 , 0 < t < 2π, with u ( i ) ( 0 ) = u ( i ) ( 2 π ) , i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of ± 10 - 7 .

Multipoint boundary value problems for discrete equations

Pavel Drábek, Harold Bevan Thompson, Christopher Tisdell (2001)

Commentationes Mathematicae Universitatis Carolinae

In this work we establish existence results for solutions to multipoint boundary value problems for second order difference equations with fully nonlinear boundary conditions involving two, three and four points. Our results are also applied to systems.

Multipoint boundary value problems for ODEs. Part II

Tadeusz Jankowski (2004)

Czechoslovak Mathematical Journal

We apply the method of quasilinearization to multipoint boundary value problems for ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic.

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