Asymptotic behavior of large solutions to H-systems with perturbations Original Research Article

Let View the MathML source be a bounded smooth domain. In this paper, we study the existence and the asymptotic behavior of solutions to the Dirichlet problem of H-systems with perturbations: View the MathML source where View the MathML source and View the MathML source. We prove that for View the MathML source denotes the 1st eigenvalue of −Δ acting on View the MathML source), (Pε) admits at least one solution View the MathML source, which blows up at exactly one point in Ω as ε→0. We also characterize the location of blow up point as the minimum point of a certain function defined on Ω, and give the exact blow up rate of View the MathML source as ε→0.