Multiple positive solutions for boundary value problems of second-order delay differential equations

We use a fixed-point index theorem in cones to study the existence of multiple positive solutions for boundary value problems of second-order delay differential equations with the form y″(x) + ƒ(x,y(x − τ)) = 0, 0 < x < 1, y(x) = 0, −τ ≤ x ≤ 0, y(1) = 0, where 0 < τ < 14 is suitably small. The main result here is the generalization of Liu and Li [1] for ordinary differential equations.

[1]  Huizhao Liu,et al.  Boundary Value Problems for Singular Second-Order Functional Differential Equations , 2000 .

[2]  K. Deimling Nonlinear functional analysis , 1985 .

[3]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[4]  Zhaoli Liu,et al.  Multiple Positive Solutions of Nonlinear Two-Point Boundary Value Problems , 1996 .

[5]  Existence of positive solutions for boundary value problems of second-order functional-differential equations. , 1998 .

[6]  Shouchuan Hu,et al.  Multiple Positive Solutions of Some Boundary Value Problems , 1994 .

[7]  D. Jiang,et al.  On the existence of nonnegative radial solutions for p-Laplacian elliptic systems , 1999 .

[8]  John W. Lee,et al.  Existence Results for Differential Delay Equations, I , 1993 .

[9]  S. Ntouyas,et al.  An existence principle for boundary value problems for second order functional differential equations , 1993 .

[10]  Haiyan Wang,et al.  On the existence of positive solutions of ordinary differential equations , 1994 .

[11]  Donal O'Regan,et al.  Existence results for differential equation—II , 1991 .

[12]  Peixuan Weng,et al.  Existence of positive solutions for boundary value problem of second-order FDE , 1999 .

[13]  Haiyan Wang,et al.  On the existence of positive solutions for semilinear elliptic equations in the annulus , 1994 .

[14]  Wen Peixuan Boundary value problems for second order mixed-type functional differential equations , 1997 .

[15]  Qingkai Kong,et al.  Boundary value problems for singular second-order functional differential equations , 1994 .