Existence of solutions for \(2n\)th order nonlinear generalized Sturm-Liouville boundary value problems (Q2720286)
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scientific article; zbMATH DE number 1610910
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Existence of solutions for \(2n\)th order nonlinear generalized Sturm-Liouville boundary value problems |
scientific article; zbMATH DE number 1610910 |
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29 September 2002
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nonlinear boundary value problems
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existence result
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upper and lower solutions
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0.9376254
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0.92514795
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0.91638535
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0.91503614
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0.91299534
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0.9110024
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Existence of solutions for \(2n\)th order nonlinear generalized Sturm-Liouville boundary value problems (English)
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The higher-order differential equation \(y^{(2n)}=f(t, y, y'', \dots , y^{(2n-2)}\), \(t\in [0,1]\), with two different sets of nonlinear boundary conditions is considered. NEWLINENEWLINENEWLINEThe authors introduce appropriate definitons of upper and lower solutions for both boundary value problems and then, assuming the existence of such functions, they prove two existence theorems. The method used is classical: a suitable modified problem is introduced and then Schauder's fixed-point theorem is employed.
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