Prediction of multiplicity of solutions of nonlinear boundary value problems: Novel application of homotopy analysis method

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A new analytical technique to solve Volterra's integral equations (2011, background): “It is important here to be said if the convergence-controller parameter c0 is chosen properly, the series (6) converges for p=1, and thus u0(x)+ +∞ ∑ m=1 um(x) (8)”
An efficient analytic approach for solving two‐point nonlinear boundary value problems by homotopy analysis method (2011, methodology): “The efficiency and reliability of the method is checked by its application to two important nonlinear exactly solvable differential equations namely nonlinear Troesch’s problem equation [37, 38] and strongly nonlinear Bratu’s equation [31, 34, 39], in addition to illustration exactly solvable differ”