University of Nevada

Title: Multiplicity results for semilinear heterogeneous problems in exterior domains of ℝ2 involving subcritical or critical nonlinearities `a la Trudinger-Moser

Abstract: Let Ω be an exterior domain in ℝ2. We prove some multiplicity results, in the Beppo-Levi space, for solutions to the following boundary value problem
−∆u = b(x) f(u) in Ω, u = 0 on ∂Ω,
where the nonnegative coefficient b(x) satisfies a suitable integrability assumption and the C1 nonlinearity f : ℝ is superlinear at zero and infinity and has subcritical or critical growth at infinity in the sense of Trudinger-Moser.