Showing papers by "Lingju Kong published in 2007"
TL;DR: In this paper, sufficient conditions are given for the existence of solutions of the following nonlinear boundary value problem with nonhomogeneous multi-point boundary condition with non-homogeneous multipoint boundary condition.
33 citations
TL;DR: In this article, a necessary and sufficient condition for the existence of symmetric positive solutions for the nonlinear boundary value problem is established. But the analysis mainly relies on the lower and upper solution method.
Abstract: We study the nonlinear boundary value problem ( ϕ ( u ′ ′ ) ) ′ ′ = f ( t , u , u ′ , u ′ ′ ) , t ∈ ( 0 , 1 ) , u ( 2 i ) ( 0 ) = u ( 2 i ) ( 1 ) = 0 , i = 0 , 1 , and obtain a necessary and sufficient condition for the existence of symmetric positive solutions. We also discuss the application of our result to the special case where f is a power function of u and its derivatives. Moreover, similar conclusions for a more general higher order boundary value problem are established. Our analysis mainly relies on the lower and upper solution method.
25 citations
TL;DR: In this paper, the existence of symmetric positive solutions of the nonlinear boundary value problem is studied and sufficient conditions are obtained for the problem to have one, any finite number, and a countably infinite number of such solutions.
16 citations
TL;DR: In this paper, necessary and sufficient conditions are obtained for the existence of symmetric positive solutions to the boundary value problem ( | u'| p − 1 u') = f ( t, u, u ', u'), t ∈ ( 0, 1 ), u ( 2 i ) ( 0 ) = u (2 i )( 1 ) = 0, i = 0, 1.
15 citations
TL;DR: In this article, the authors studied the right-definite separated half-linear Sturm-Liouville eigenvalue problem and proved that the real eigenvalues of the problem depend smoothly on the equation, but may have jump discontinuities with respect to the boundary condition.
Abstract: We study the right-definite separated half-linear Sturm–Liouville eigenvalue problems. It is proved that the $n$th real eigenvalue of the problem depends smoothly on the equation, but may have jump discontinuities with respect to the boundary condition. Formulae are found for the derivatives of the $n$th real eigenvalue with respect to all parameters: the endpoints, the boundary condition and the coefficient functions, whenever they exist. Monotone properties and a comparison result for real eigenvalues are deduced as consequences. The generalized Prüfer transformation and the implicit function theorem in Banach spaces play key roles in the proofs.
3 citations