Singular nonresonant Dirichlet boundary value problems and quadratic forms. (Q2763888)
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scientific article; zbMATH DE number 1693363
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Singular nonresonant Dirichlet boundary value problems and quadratic forms. |
scientific article; zbMATH DE number 1693363 |
Statements
2001
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boundary value problems
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existence results
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singular nonresonant Dirichlet boundary data
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Singular nonresonant Dirichlet boundary value problems and quadratic forms. (English)
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Existence results are presented for nonresonant Dirichlet second-order boundary value problems of the form \(y^{\prime\prime}+a(t)y=f(t,y)\) a.e. on \([0,1]\), \(y(0)=y(1)=0\), where \(f\):\([0,1]\times \mathbb{R}\rightarrow \mathbb{R}\) is a \(L^1\)-Carathéodory function, \(a\in L^1_{\text{loc}}(0,1)\), \(a>0\) a.e. on [0,1] and \(\int^1_0x(1-x)a(x)\,dx<\infty\).
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