Bifurcation theory and radial solutions to elliptic boundary value problems (Q1344028)
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scientific article; zbMATH DE number 720455
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bifurcation theory and radial solutions to elliptic boundary value problems |
scientific article; zbMATH DE number 720455 |
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Bifurcation theory and radial solutions to elliptic boundary value problems (English)
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9 February 1995
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The author explains how to use basic tools from general bifurcation theory and properties of the solutions to the initial value problems, in order to establish bounds on the number of radial solutions to the elliptic boundary value problem: \(\Delta u + \lambda g (\| x \|, u) = p(\| x \|)\) for \(\| x \| < 1\), \(u(x) = 0\) for \(\| x \| = 1\). Three cases are discussed: 1) the derivative of \(g = g(u)\) crosses the eigenvalues of \(- \Delta\); 2) \(g\) is superlinear with nonlinearity with critical growth; 3) a problem with jumping nonlinearities.
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semilinear elliptic equations
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bounds on the number of radial solutions
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0.787856936454773
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