On the solvability of a boundary value problem for $p$-Laplacian differential equations

Abstract

Using barrier strip conditions, we study the existence of $C^2[0,1]$-solutions of the boundary value problem $(\phi_p(x^{\prime}))^{\prime}=f(t,x,x^{\prime}),$ $x(0)=A,\ x^{\prime}(1)=B,$ where $\phi_p(s)=s|s|^{p-2},\ p>2$. The question of the existence of positive monotone solutions is also affected