Iterative technique for third-order differential equation with three-point nonlinear boundary value conditions

Lin, Xiuli; Zhen, Zhao

doi:10.14232/ejqtde.2016.1.12

Cited by 53 publications

(30 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Under the self-similar transformation (2.4), the Riemann problem (1.1) and (1.7) can be reduced into the boundary value problem [34,35] of ordinary differential equations as follows:…”

Section: The Solutions Of the Riemann Problem (11) And (17)mentioning

confidence: 99%

Construction of global solutions for a symmetric system of Keyfitz–Kranzer type with three piecewise constant states

2019

Self Cite

View full text Add to dashboard Cite

The exact solutions of the Riemann problem for a symmetric system of Keyfitz-Kranzer type are obtained in fully explicit forms. Furthermore, the global solutions of the double Riemann problems are also constructed explicitly when the initial data are taken to be three piecewise constant states. During the process of constructing the global solutions, all occurring wave interactions have been dealt with in detail by using the method of characteristics. In addition, it is shown that the Riemann solutions are stable with respect to the specific small perturbations of the Riemann initial data.

show abstract

“…Under the self-similar transformation (2.4), the Riemann problem (1.1) and (1.7) can be reduced into the boundary value problem [34,35] of ordinary differential equations as follows:…”

Section: The Solutions Of the Riemann Problem (11) And (17)mentioning

confidence: 99%

Construction of global solutions for a symmetric system of Keyfitz–Kranzer type with three piecewise constant states

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the aspect of mathematical theory and application, to obtain further information of the relative natural phenomena, many authors are interested in the existence and properties of solutions for fractional differential models [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and many analytical techniques and methods have been developed to solve various differential equations, such as iterative methods [28][29][30][31][32][33][34][35][36][37], the Mawhin continuation theorem for resonance [38][39][40], the topological degree method [41,42], the fixed point theorem [43][44][45][46][47][48][49][50][51][52][53][54][55], the variational method [56][57][58]…”

Section: Introductionmentioning

confidence: 99%

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

Zhang

Liu

et al. 2018

Bound Value Probl

View full text Add to dashboard Cite

In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitable upper and lower solutions and employing Schauder's fixed point theorem, the conditions for the existence of positive solutions are established and the asymptotic analysis for the obtained solution is carried out. In our work, the nonlinear function involved in the equation not only contains fractional derivatives of unknown functions but also has a stronger singularity at some points of the time and space variables.

show abstract

“…The mainly techniques authors need are fixed point theory, variational method, and global bifurcation techniques. Also, ordinary differential equations and partial differential equations involving nonlocal boundary conditions have been studied extensively in recent years, see [14][15][16][17][18][19][20][21][22], including integral boundary conditions and multipoint boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

The Exact Iterative Solution of Fractional Differential Equation with Nonlocal Boundary Value Conditions

Mao

Zhen

Wang

2018

Journal of Function Spaces

Self Cite

View full text Add to dashboard Cite

We deal with a singular nonlocal fractional differential equation with Riemann-Stieltjes integral conditions. The exact iterative solution is established under the iterative technique. The iterative sequences have been proved to converge uniformly to the exact solution, and estimation of the approximation error and the convergence rate have been derived. An example is also given to demonstrate the results.

show abstract

Iterative technique for third-order differential equation with three-point nonlinear boundary value conditions

Cited by 53 publications

References 0 publications

Construction of global solutions for a symmetric system of Keyfitz–Kranzer type with three piecewise constant states

Construction of global solutions for a symmetric system of Keyfitz–Kranzer type with three piecewise constant states

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

The Exact Iterative Solution of Fractional Differential Equation with Nonlocal Boundary Value Conditions

Contact Info

Product

Resources

About