Nonlinear Singular Boundary Value Research Articles

Existence and uniqueness of positive solutions for fourth-order nonlinear singular continuous and discrete boundary value problems

Using the mixed monotone method we establish the existence and uniqueness of positive solutions for some fourth-order nonlinear singular continuous and discrete boundary value problem. The theorems obtained are very general and complement previously known results.

Multiple positive solutions for some four-point boundary value problems with p-Laplacian

This paper is devoted to the existence of multiple positive solutions for some nonlinear singular four-point boundary value problems with p-Laplacian. Under appropriate assumptions on the nonlinear terms, by applying several known fixed point theorems, sufficient conditions for the existence of at least three positive solutions are established.

Multiplicity of Positive Periodic Solutions of Singular Semipositone Third-Order Boundary Value Problems

We establish the existence of multiple positive solutions for a singular nonlinear third-order periodic boundary value problem. We are mainly interested in the semipositone case. The proof relies on a nonlinear alternative principle of Leray-Schauder, together with a truncation technique.

Solutions for higher-order dynamic equations on time scales

Let T be a time scale. We study the existence of positive solutions for the nonlinear four-point singular boundary value problem with higher-order p-Laplacian dynamic equations on time scales. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear four-point singular boundary value problem with p-Laplacian operator are obtained.

An non-uniform mesh cubic spline TAGE method for non-linear singular two-point boundary value problems

We report a non-uniform mesh cubic spline method of accuracy for the solution of non-linear singular two-point boundary value problems. The application of two-parameter alternating group explicit (TAGE) and Newton–TAGE iteration methods which are suitable for use on parallel computers is discussed. The error analysis for TAGE iteration method is discussed in detail. The numerical results confirm the utility of proposed cubic spline TAGE iteration methods.

A boundary layer problem arising in gravity-driven laminar film flow of power-law fluids along vertical walls

A rigorous mathematical analysis is given for a boundary layer problem for a third-order nonlinear ordinary differential equation, which arises in gravity-driven laminar film flow of power-law fluids along vertical walls. Firstly, the problem is transformed into a singular nonlinear two-point boundary value problem of second order. Next, the latter is proved to have a unique positive solution, for which some estimates are established. Finally, the result above-mentioned is turned over to the original problem. The conclusion of this paper is that the boundary layer problem has a unique normal solution if the power-law index is less than or equal to one and a generalized normal solution if the power-law index is greater than one. Also the asymptotic behavior of the normal solution at the infinity is displayed.

Positive solutions of nonlinear elliptic singular boundary value problems in a ball

This paper deals with existence of positive solutions of non-linear elliptic singular boundary value problems in a ball. It is shown that results of Grandall et al. [1] and [2] follow as special cases of our results proved in this article.

The Decomposition Method For Solving Of A Class Of Singular Two-Point Boundary Value Problems

In this paper, a class of nonlinear singular two-point boundary value problems are solved by using Adomian's decomposition methods. The approximate solution of this problem is calculated in the form of series with easily computable components. Finally, we give a nonlinear numerical example.

The existence of positive solutions of nonlinear singular second-order boundary value problems

In this paper, we investigate the existence of positive solutions of a second-order singular boundary value problem by constructing upper and lower solutions and combined them with properties of the consequent mapping.

A necessary and sufficient condition for singular nonlinear second-order boundary value problems to have positive solutions

In this paper the following result is obtained: Suppose f(g,u,v) is nonnegative, continuous in (a, 6) ×R+ ×R+; f may be singular at κ = a(and/or κ = b) and υ = 0; f is nondecreasing on u for each κ,υ,nonincreasing on υ for each κ,u; there exists a constant q e (0,1) such that $$ < $$ .

Positive solutions to certain classes of singular nonlinear second order boundary value problems

This paper is devoted to the problem of existence of solutions to the nonlinear singular two point boundary value problem\(\tfrac{1}{{p\left( t \right)}}(p(t)y')' + q(t)f(t,{\text{ }}y,{\text{ }}p(t)y') = 0,{\text{ }}0< t< 1\), withy satisfying either “mixed” boundary datay(1)=Limy→0+p(t)y′(t)=0 or “dirichlet” boundary datay(0)=y(1)=0. Throughout our nonlinear termqf is allowed to be singular att=0,t=1,y=0 and/orpy′=0.

A singular perturbation nonlinear boundary value problem and the 𝐸-condition for a scalar conservation law

A singular perturbation nonlinear boundary value problem and the 𝐸-condition for a scalar conservation law

Computationally Useful Bounds for Singular Nonlinear Second Order Boundary Value Problems

Bounds are found for a solution y, to the ordinary differential equation $(r^k p(r,y)y')' + r^k q(r,y) = 0(' = {d / {dr}})$, with initial conditions $y(0) = y_0 > 0$, $y'(0) = 0$. The principal assumptions are that $k \geqq 1,q(r,y(r))$ is decreasing for $0 \leqq r \leqq a$ and $q(a,y(a)) \geqq 0$. Also, r-independent bounds on p and q are assumed to exist. Lower bounds on y valid for $0 \leqq r \leqq a$ are found, and, also, upper bounds valid on a possibly smaller interval. They will be applied to Bessel’s equation to show how close they are. The bounds will further be applied to boundary value problems arising in gas glow discharge theory and tubular chemical reactor theory.

Solution of a nonlinear two point boundary value problem

A class of singular second order nonlinear two-point boundary value problems is solved, by introducing a finite element approximation which preserves an assumed monotonicity condition in the discrete equations obtained.

Singular perturbations and nonlinear parabolic boundary value problems

Singular perturbations and nonlinear parabolic boundary value problems