Pointwise solution bounds for a class of singular diffusion problems in physiology

On solvability of derivative dependent doubly singular boundary value problems

“…Such problems arise very frequently in applied sciences [5,6,11] and also in physiological studies ( [1][2][3]9] and references as there in). In case f is independent of y , existence-uniqueness results have been established by several researchers [7, 12-14, 16, 20].…”

On a Class of Weakly Regular Singular Two-Point Boundary Value Problems, II

“…Since u(x; k) will not change sign for 0<k<k 1 and u(0) 0, we get that y(x) 0 for 0<k<k 1 , provided B 0.…”

“…Numerical methods have been discussed by several authors [3 9]. Recently Asaithambi and Garner [1] have studied numerically the differential equation (1) on (0, 1] with the more general boundary conditions then the above problem (1) (2) can be reduced to a regular one by a change of variable:…”

Wavelet Galerkin method for solving nonlinear singular boundary value problems arising in physiology

“…The boundary value problem (1)-(3) with r ¼ 0; 1; 2 and a ¼ 0 arise in the study of various tumor growth problems, see [15][16][17][18][19], with linear f ðx; yÞ and with nonlinear f ðx; yÞ of the form:…”