Global bifurcation and constant sign solutions of discrete boundary value problem involving p -Laplacian

Advances in Difference Equations

article

Ye, Fumei¹ 

[1] Department of Mathematics, Northwest Normal University

关键词: Discrete p -Laplacian;    Principal eigenvalue;    Unilateral global bifurcation;    Constant sign solutions;   

DOI  :  10.1186/s13662-021-03309-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We study the unilateral global bifurcation result for the one-dimensional discrete p-Laplacian problem$$ \textstyle\begin{cases} -\Delta [\varphi _{p}(\Delta u(t-1))]=\lambda a(t)\varphi _{p}(u(t))+g(t,u(t), \lambda ),\quad t\in [1,T+1]_{Z}, \\ \Delta u(0)=u(T+2)=0, \end{cases} $$ where$\Delta u(t)=u(t+1)-u(t)$ is a forward difference operator,$\varphi _{p}(s)=|s|^{p-2}s$ ( $11$ be an integer, Z denote the integer set for$m, n\in Z$ with$m0$ for$s\neq 0$ .

【 授权许可】

CC BY