We discuss the linear conjugate boundary value problems on the unit circle and the real axis. We obtain some Fredholm integral equations. Using thess equations we discuss the solvable conditions on these problems and ...We discuss the linear conjugate boundary value problems on the unit circle and the real axis. We obtain some Fredholm integral equations. Using thess equations we discuss the solvable conditions on these problems and we also give a direct method for the extension problems on the real axis.展开更多
This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t&l...This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]展开更多
By the fxed point index theory, the existence of one, two and three positive solutions to(k, n-k) conjugate boundary value problems is obtained, where n 】 2, 1 ≤ k ≤ n-1, the nonlinear term may be noncontinuous and...By the fxed point index theory, the existence of one, two and three positive solutions to(k, n-k) conjugate boundary value problems is obtained, where n 】 2, 1 ≤ k ≤ n-1, the nonlinear term may be noncontinuous and singular at any point of [0,1]. Our results extend some of the existent results.展开更多
基金Supported by the National Natural Science Foundation of China (10471107)
文摘We discuss the linear conjugate boundary value problems on the unit circle and the real axis. We obtain some Fredholm integral equations. Using thess equations we discuss the solvable conditions on these problems and we also give a direct method for the extension problems on the real axis.
基金Supported by the NSF of Guangdong Province!( 980 0 1 8) Higher Education Bureau!( 1 99873)
文摘This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]
基金supported by the National Natural Science Foundation of China(11171088)the Natural Science Foundation of Hebei Province(A2013208108)the Foundation of Hebei University of Science and Technology(XI2013060)
文摘By the fxed point index theory, the existence of one, two and three positive solutions to(k, n-k) conjugate boundary value problems is obtained, where n 】 2, 1 ≤ k ≤ n-1, the nonlinear term may be noncontinuous and singular at any point of [0,1]. Our results extend some of the existent results.
