Global continuum and multiple positive solutions to a p-Laplacian boundary-value problem

Electronic Journal of Differential Equations

关键词: Upper and lower solution;    positive solution;    p-Laplacian;    uniqueness;    multiplicity;   

DOI  :  

来源: DOAJ

【 摘 要 】

A p-Laplacian boundary-value problem with positive nonlinearityis considered. The existence of a continuum of positive solutionsemanating from $(lambda,u)=(0,0)$ is shown, and it can be extendedto $lambda=infty$. Under an additional condition on the nonlinearity,it is shown that the positive solution is unique for any $lambda>0$;thus the continuum $mathcal{C}$ is indeed a continuous curve globallydefined for all $lambda>0$. In addition, by the upper and lower solutionsmethod, existence of three positive solutions is established under someconditions on the nonlinearity.

【 授权许可】

Unknown