## The monotone iterative technique for three-point second-order integrodifferential boundary value problems with $$p$$-Laplacian.(English)Zbl 1149.65098

The authors consider a problem of the existence of the extremal positive concave pseudosymmetric solutions $$x(t),\,0<t<1,$$ to a scalar nonlinear integro-ordinary differential equation with the main part $$(x'(t)| x'(t)| ^{p-2})'$$, where $$p>1$$, and with the conditions $$x(0)=0$$, $$x(\eta)=x(1)$$, $$0<\eta<1$$. Some monotone iterative operator is proposed and convergence of corresponding iterations to the desired solutions at some assumptions of equation’s functions is proved. An example demonstrates the main result.

### MSC:

 65R20 Numerical methods for integral equations 45J05 Integro-ordinary differential equations 45G10 Other nonlinear integral equations
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### References:

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