Remarks on the range properties of certain semilinear problems of Landesman-Lazer type (Q5937232)
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scientific article; zbMATH DE number 1618713
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Remarks on the range properties of certain semilinear problems of Landesman-Lazer type |
scientific article; zbMATH DE number 1618713 |
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Remarks on the range properties of certain semilinear problems of Landesman-Lazer type (English)
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12 July 2001
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Dirichlet problem
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bounded nonlinearities
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The authors consider the Dirichlet problem NEWLINE\[NEWLINEu''(t)+ u(t)+ g(u'(t))= f(t),\quad u(0)= u(\pi)= 0.NEWLINE\]NEWLINE It is assumed that \(g\) is continuous, has finite limits \(g(+\infty)\), \(g(-\infty)\), and \(g(-\infty)< g(s)< g(+\infty)\) for all \(s\). The case of odd and increasing \(g\) with some asymptotic conditions is dealt with in more detail. The structure of the set of continuous functions \(f\) is studied for which the problem is solvable.
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