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On a class of quasilinear eigenvalue problems in \(\mathbb R^N\). (English) Zbl 1161.35456

Summary: We study an eigenvalue problem in \(\mathbb R^N\) which involves the \(p\)-Laplacian \((p>N\geq 2)\) and the nonlinear term has a global (\(p-1\))-sublinear growth. The existence of certain open intervals of eigenvalues is guaranteed for which the eigenvalue problem has two nonzero, radially symmetric solutions. Some stability properties of solutions with respect to the eigenvalues are also obtained.

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J60 Nonlinear elliptic equations
47J30 Variational methods involving nonlinear operators
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