Positive solutions for one-dimensional third-order p-Laplacian boundary value problems

Abstract

Abstract In this paper, we give improved results on the existence of positive solutions for the following one-dimensional p-Laplacian equation with nonlinear boundary conditions: { ( ϕ p ( y ″ ) ) ′ + b ( t ) g ( t , y ( t ) ) = 0 , 0 1 $p >1 $ . Constructing an available integral operator and combining fixed point index theory, we establish some optimal criteria for the existence of bounded positive solutions. The interesting point of the results is that the term b ( t ) $b ( t ) $ may be singular at t = 0 $t=0$ and/or t = 1 $t=1$ . Moreover, the nonlinear term g ( t , y ) $g(t, y)$ is also allowed to have singularity at y = 0 $y=0$ . In particular, our results extend and unify some known results.

Keywords

• cone
• existence
• positive solution
• maximum principle