Third order differential equations with integral boundary conditions

A family of singular ordinary differential equations of the third order with an integral boundary condition

“…Then, by derivation of (1.2) and by using the property (2.4) we have 14) and the boundary condition y (0) = 0 holds. Therefore, from (2.14) we have…”

“…There are results on the existence and asymptotic estimates of solutions for third order ordinary differential equations with singularly perturbed boundary value problems, which depend on a small positive parameter, see, for example [1][2][3], on third order ordinary differential equations with singularly perturbed boundary value problems and with nonlinear coefficients or boundary conditions, see for example [4][5][6][7], on third order ordinary differential equations with nonlinear boundary value problems, see for example [8,9], on existence results for third order ordinary differential equations, see for example [10][11][12], and particularly third order ordinary differential equations with integral boundary conditions, see for example [13][14][15][16][17][18][19][20][21].…”

The lower and upper solution method for three-point boundary value problems with integral boundary conditions on a half-line

“…Multi-point boundary value problems for second-order differential equations in a finite interval and on an infinite interval included the large amount of priori work and many excellent results are obtained by using Avery-Peterson fixed point theorem, shooting method, lower and upper solution method, Leray-Schauder continuation theorem and so on, see for instance [1][2][3][4][5][6][7][8][9][10][11][12][13]15]. Meanwhile, BVPs with integral boundary conditions for ordinary differential equations have been extensively examined by many authors, for example see [11][12][13][14][15][16]. But, there is a little work related to boundary value problems with integral boundary conditions on an infinite interval.…”

On The Existence Of Multiple Solutions Of A Class Of Second-order Nonlinear Two-point Boundary Value Problems

“…The second factor motivating our work is the lack of theoretical framework capable of obtaining solutions. The great numbers of methods which involve upper and lower solutions being based on fixed-point theory [26][27][28][29][30][31][32][33][34][35][36][37] illustrate only the existence of some classes of solution without providing a real procedure to obtain them. Of course this is difficult task and sometimes impossible, however the present paper gives a proof, which is constructive in nature, for existence of multiple solutions of the problems (1)- (2) and (3)- (4), and obtain all branches of solutions (if they exist) at the same time.…”