3 papers
math.AP2024
Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions
Tetsutaro Shibata
We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions and bifurcation curves $λ(α…
math.AP2023
Global bifurcation curves of nonlocal elliptic equations with oscillatory nonlinear term
Tetsutaro Shibata
We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with oscillatory nonlinear term. We establish the precise asymptotic formulas for the bifurcation curves $…
math.AP2021
Asymptotic behavior of bifurcation curves of one-dimensional nonlocal elliptic equations
Tetsutaro Shibata
We study the one-dimensional nonlocal elliptic equation \begin{eqnarray*} -\left(\int_0^1 \vert u(x)\vert^p dx + b\right)^q u''(x) &=& λu(x)^p, \quad x \in I:= (0,1), \ u(x) > 0, \…