Semilinear elliptic equations with the primitive of the nonlinearity interacting with the first eigenvalue (Q1176899)
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scientific article; zbMATH DE number 12670
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Semilinear elliptic equations with the primitive of the nonlinearity interacting with the first eigenvalue |
scientific article; zbMATH DE number 12670 |
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Semilinear elliptic equations with the primitive of the nonlinearity interacting with the first eigenvalue (English)
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25 June 1992
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The authors study the problem \(-\Delta u=f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\) by variational methods when \(f\) interacts with the first eigenvalue in a very weak sense. (The conditions are on the primitive of \(F\).) They discuss when the corresponding functional is coercive and when the mountain pass theorem can be applied.
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coercivity
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mountain pass theorem
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