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http://dx.doi.org/10.4134/BKMS.b190227

NODAL SOLUTIONS FOR AN ELLIPTIC EQUATION IN AN ANNULUS WITHOUT THE SIGNUM CONDITION  

Chen, Tianlan (Department of Mathematics Northwest Normal University)
Lu, Yanqiong (Department of Mathematics Northwest Normal University)
Ma, Ruyun (Department of Mathematics Northwest Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 331-343 More about this Journal
Abstract
This paper is concerned with the global behavior of components of radial nodal solutions of semilinear elliptic problems -Δv = λh(x, v) in Ω, v = 0 on ∂Ω, where Ω = {x ∈ RN : r1 < |x| < r2} with 0 < r1 < r2, N ≥ 2. The nonlinear term is continuous and satisfies h(x, 0) = h(x, s1(x)) = h(x, s2(x)) = 0 for suitable positive, concave function s1 and negative, convex function s2, as well as sh(x, s) > 0 for s ∈ ℝ \ {0, s1(x), s2(x)}. Moreover, we give the intervals for the parameter λ which ensure the existence and multiplicity of radial nodal solutions for the above problem. For this, we use global bifurcation techniques to prove our main results.
Keywords
Nodal solutions; elliptic equation; bifurcation;
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