Nontrivial solutions to some semilinear sixth-order differential equations (Q2762954)
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scientific article; zbMATH DE number 1689805
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nontrivial solutions to some semilinear sixth-order differential equations |
scientific article; zbMATH DE number 1689805 |
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16 January 2002
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variational method
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minimization
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mountain-pass theorem
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homoclinic solution
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0.96852237
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0.9476742
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0.9356432
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0.9320227
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0.9300381
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0.92271155
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Nontrivial solutions to some semilinear sixth-order differential equations (English)
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The author considers a two-point boundary value problem for a 6th-order semilinear ordinary differential equation. Applying variational methods, he proves the existence of a periodic solution and more precisely, an \(m\)-multiplicity result under several conditions. The existence of a homoclinic solution to a sixth-order equation with non-\(C^{\infty}\) smooth nonlinearity is announced in theorem 3.
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