Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.02.28
  • Accepted : 2019.07.08
  • Published : 2020.03.31
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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

Acknowledgement

Supported by : NSFC

This work was financially supported by NSFC No. 11801453, No. 11671322, and No. 11901464.

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