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

We study the solvability of the boundary value problem ( p(x 0 )) 0 = f(t;x;x 0 ); x(0) = A; x 0 (1) = B; where p(s) = sjsjp 2, using the barrier strip type arguments. We establish the existence of C2(0; 1)-solutions, restricting our considerations to p2 (1; 2). The existence of positive monotone solutions is also considered. ( (x 0 )) 0 = q(x 0 (t))f(t;x(t);x 0 (t)); with nonlinear functional boundary conditions, and for the equation ( (x 0 )) 0 = f(t;x(t);x( (t));x 0 (t));

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