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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 \(\lambda\).

MSC:
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
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