### Dang Q. Dang L.Q.

## Existence results and iterative method for solving a fully third order nonlinear differential equation with integral boundary condition

### Reporter: Dang Q.

Existence results and iterative method for solving a fully third order nonlinear differential equation with integral boundary condition

Dang Quang A1, Dang Quang Long2

1 Center for Informatics and Computing, VAST

2 Institute of Information Technology, VAST

We consider a boundary value problem for fully third order differential equation u(4)(t)=f(t,u(t),u’(t),u’’(t)) with three boundary conditions including one integral boundary condition. For the particular case f = f(u(t)), very recently in [1] the existence of positive solutions was studied by employing the fixed point theory on cones. In this paper, by the method developed in [2]-[5] we establish the existence, uniqueness and positivity of solution and propose an iterative method for finding the solution. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the iterative method.

References

1. Guendouz C., Haddouchi F., Benaicha S., Existence of positive solutions for a nonlinear third-order integral boundary value problem, arXiv:1801.08990v1 [math.CA] 26 Jan 2018.

2. Dang, Q.A., Ngo, K.Q.: Existence results and iterative method for solving the cantilever beam equation with fully nonlinear term, Nonlinear Anal. Real World Appl. 36, (2017) 56-68.

3. Dang, Q.A., Dang, Q.L., Ngo, K.Q.: A novel efficient method for nonlinear boundary value problems, Numer. Algor., 76, 427-439 (2017).

4. Dang, Q.A., Ngo, K.Q.: New Fixed Point Approach For a Fully Nonlinear Fourth Order Boundary Value Problem, Bol. Soc. Paran. Mat. 36(4), 209-223 (2018).

5. Dang Q.A, Dang Q. L., A simple efficient method for solving sixth order nonlinear boundary value problems, Comp. Appl. Math. DOI 10.1007/s40314-018-0643-1 (2018).

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