Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation
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DOI: 10.1016/j.jde.2017.03.019
Abstract: Abstract Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation. The expansions of such singular… read more here.
Keywords: singular radial; solutions prescribed; biharmonic equation; radial entire ... See more keywords
Solutions with prescribed mass to Kirchhoff equations: generic double-behaviour nonlinearities
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DOI: 10.1088/1361-6544/ae0b26
Abstract: In this paper, we study the Kirchhoff equation {−(a+b∫ℝ3|∇u|2dx)Δu+λu=f(u), x∈ℝ3,∫ℝ3|u|2dx=c2, x∈ℝ3,(λ,u)∈ℝ×H1(ℝ3), where a,b,c>0, λ∈R is unknown as a Lagrange multiplier. We provide generic assumptions about the nonlinearity f(u), which correspond to the L2-subcritical, L2-critical, L2-supercritical, and Sobolev… read more here.
Keywords: equations generic; generic double; mass kirchhoff; solutions prescribed ... See more keywords