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Critical superlinear Ambrosetti-Prodi problems. (English) Zbl 0958.35055
Summary: We consider the existence of multiple solutions for problem \[ -\Delta u=\lambda u+u_+^{2^*-1}+ f(x)\text{ in }\Omega,\;u=0\text{ on }\partial\Omega, \] where \(2^*=2N/(N-2)\), \(N\geq 3\) is the critical Sobolev exponent and \(\lambda>0\) is a constant with either \(\lambda\neq\lambda_1\) or \(\lambda=\lambda_1\), where \(\lambda_k\), \(k=1,2,\dots\) are eigenvalues of \((-\Delta, H^1_0(\Omega))\). The local bifurcation from \(\lambda=\lambda_k\) is also investigated.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35B32 Bifurcations in context of PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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