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

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

Solvability of singular second-order initial value problems

This article concerns the solvability of the initial-value problem x''=f(t,x,x'), x(0)=A, x'(0)=B, where the scalar function f may be unbounded as $t\to 0$. Using barrier strip type arguments, we establish the existence of monotone and/or positive solutions in $C^1[0,T]\cap C^2(0,T]$

Existence of solutions to first-order singular and nonsingular initial value problems

Under barrier strip type arguments we investigate the existence of global solutions to the initial value problem $x'=f(t,x,x')$, $x(0)=A$, where the scalar function $f(t,x,p)$ may be singular at $t=0$

Solvability of a second-order singular boundary-value problem

Using the barrier strips technique, we study the existence of solutions to the boundary-value problem $$displaylines{ x''=f(t,x,x'),quad tin(0,1),cr x'(0)=A,quad x(1)=Bx'(1)+C, }$$ where the scalar function f may be singular at t=0

Existence of solutions of nonlinear third-order two-point boundary value problems

We study various two-point boundary value problems for the equation $x'''=f(t,x,x',x'')$. Using barrier strips type conditions, we give sufficient conditions guaranteeing positive or non-negative, monotone, convex or concave $C^3[0,1]$-solutions

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

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

The barrier strip technique for a boundary value problem with p-Laplacian

We study the solvability of the boundary value problem $$(phi_p(x'))'=f(t,x,x'),quad x(0)=A,;x'(1)=B,$$ where $phi_p(s)=s|s|^{p-2}$, using the barrier strip type arguments. We establish the existence of $C^2[0,1]$-solutions, restricting our considerations to $pin(1,2]$. The existence of positive monotone solutions is also considered

Minimal and maximal solutions for two-point boundary-value problems

In this article we consider a boundary-value problem for the equation ${f(t,x,x',x'')=0}$ with mixed boundary conditions. Assuming the existence of suitable barrier strips, and using the monotone iterative method, we obtain the minimal and maximal solutions