Existence and nonexistence results for a class of non-self-adjoint fourth-order singular boundary value problems arising in real life

In this work, we propose the following fourth-order non-self-adjoint SBVPs to investigate 1/r(?? ){r(??)[1/r(??)(r(??)??')']'}'=1/2r(??)(??'??'(2)+2????'??'')+??G(r),for 0 < r < 1, where ?? is the parameter, ??(r) = pr(2??-2), p is an element of R+, G(r) is an element of L-1[0,1] such that M-1 >= G(r) >= M > 0 and ?? > 1 with respect to three different homogeneous boundary conditions. By using monotone iterative technique we show the existence of atleast one solution, which depends on the parameter??. We report presence of two solutions computationally. We show the sign of the both solutions and derive the estimations of the parameter??which indicates the region of non existence. To validate the estimations of??we propose an iterative technique with the help of Greens function. We place the numerical results as an evidence of our derived theoretical result