Sentence examples for allowed to be singular from inspiring English sources

The nonlinearity f in (2) allowed to be singular in its second and third variable.

where λ > 0 and the nonlinear term f ( x, u ) is allowed to be singular on ∂ Ω.

c ( t ) ≢ 0 is allowed to be singular at t = 0, 1, and f may be singular at u = 0.

By using the sequential technique and regularization on a cone, some new existence results are obtained for the case where the nonlinearity is allowed to be singular with respect to both time and space variables.

The fractional orders are involved in the nonlinearity of the boundary value problem, and the nonlinearity is allowed to be singular with respect to not only the time variable but also to the space variable.

First, the boundary value problem has a more general form, in which p, q are allowed to be singular at (t=0, 1) and f, g may be singular at (x=0).

By using fixed point theorem in cone, Yuan et al. [26] studied the following coupled system of nonlinear singular boundary value problem: (1.2). are allowed to be superlinear and are singular at and/or.

The operator (H 0)) maybe singular with the possible singular end point (y=0) since (U /U_{0}) is allowed to be not integrable on ((0,1]).

Firstly, the nonlinearity f is allowed to depend on higher derivatives of unknown functions, and we allow f to be singular at (t=0,1) and (x_{i}=0 (i=0,1,ldots,n-2)).

Firstly, the nonlinearity f is allowed to depend on higher derivatives of unknown function (x t)) up to (n-2) order, and we allow f to be singular at (t=0,1).

We allow and to be singular at,, and also and/or.