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Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions

Tetsutaro Shibata

Abstract

We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions $u_λ$ and bifurcation curves $λ(α)$, where $α:= \Vert u_λ\Vert_\infty$.

Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions

Abstract

We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions and bifurcation curves , where .
Paper Structure (3 sections, 49 equations)

This paper contains 3 sections, 49 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem 1.1 and Preliminaries
  3. Proof of Theorem 1.2