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The Lane-Emden function and nonlinear eigenvalues problems. (English) Zbl 1180.35401

Summary: We consider a semilinear elliptic eigenvalues problem on a ball of \(\mathbb R^n\) and show that all the eigenfunctions and eigenvalues can be obtained from the Lane-Emden function.

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J61 Semilinear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J20 Variational methods for second-order elliptic equations
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