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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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