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Critical singular problems on unbounded domains. (English) Zbl 1128.35047

Summary: We present some existence results for the following problem: \(-\Delta u=a(x)g(u)+u|u|^{2*-2}, x\in{\mathbb R}^N (N\geq3),\;u\in D^{1,2}({\mathbb R}^N)\), where the function \(a\) is a sign-changing function with a singularity at the origin and \(g\) has growth up to the Sobolev critical exponent \(2^*=2N/(N-2)\).

MSC:

35J60 Nonlinear elliptic equations
35B33 Critical exponents in context of PDEs
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