Monotone iterative method and regular singular nonlinear BVP in the presence of reverse ordered upper and lower solutions

Verma, Amit K.

Electronic journal of differential equations, Tome 2012 (2012)

Résumé

Monotone iterative technique is employed for studying the existence of solutions to the second-order nonlinear singular boundary value problem

$ -\big(p(x)y'(x)\big)'+p(x)f\big(x,y(x),p(x)y'(x)\big)=0 $

for $0$ and $y'(0)=y'(1)=0$. Here $p(0)=0$ and $x p'(x)/p(x)$ is analytic at $x=0$. The source function $f(x,y,py')$ is Lipschitz in $py'$ and one sided Lipschitz in $y$. The initial approximations are upper solution $u_0(x)$ and lower solution $v_0(x)$ which can be ordered in one way $v_0(x)\leq u_0(x)$ or the other $u_0(x)\leq v_0(x)$.

Détail

Classification : 34B16
Keywords: monotone iterative technique, lower and upper solutions, Neumann boundary conditions