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On the multiplicity of the solutions of the equation \(-\Delta u=\lambda \cdot f(u)\). (English) Zbl 1330.35279
Summary: Let \(\Omega\) be a bounded open subset of \(\mathbb{R}^n\). We discuss conditions on the continuous function \(f:\mathbb{R}\to\mathbb{R}\) ensuring that the problem \(-\Delta u=\lambda f(u)\) admits unboundedly many weak solutions in \(H^1_0(\Omega)\) for any positive real \(\lambda\).

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
47J30 Variational methods involving nonlinear operators
Full Text: DOI
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