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.
Reviewer: Vladimir Gorbunov (Ul’yanovsk)
MSC:
| 65R20 | Numerical methods for integral equations |
| 45J05 | Integro-ordinary differential equations |
| 45G10 | Other nonlinear integral equations |
Keywords:
integro-ordinary differential equations; existence; extremal positive concave pseudosymmetric solution; iterative technique; numerical exampleReferences:
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