Displaying similar documents to “Resonant problem for a class of bvps on the half-line.”

Unbounded solutions of BVP for second order ODE with p -Laplacian on the half line

Yuji Liu, Patricia J. Y. Wong (2013)

Applications of Mathematics

Similarity:

By applying the Leggett-Williams fixed point theorem in a suitably constructed cone, we obtain the existence of at least three unbounded positive solutions for a boundary value problem on the half line. Our result improves and complements some of the work in the literature.

Solutions of a multi-point boundary value problem for higher-order differential equations at resonance. (II)

Yuji Liu, Weigao Ge (2005)

Archivum Mathematicum

Similarity:

In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equation x ( n ) ( t ) = f ( t , x ( t ) , x ' ( t ) , ⋯ , x ( n - 1 ) ( t ) ) + e ( t ) , 0 < t < 1 , ( * ) and the following multi-point boundary value conditions 1 * - 1 x ( i ) ( 0 ) = 0 f o r i = 0 , 1 , ⋯ , n - 3 , x ( n - 1 ) ( 0 ) = α x ( n - 1 ) ( ξ ) , x ( n - 2 ) ( 1 ) = ∑ i = 1 m β i x ( n - 2 ) ( η i ) . * * Sufficient conditions for the existence of at least one solution of the BVP ( * ) and ( * * ) at resonance are established. The results obtained generalize and complement those in [13, 14]. This paper is directly motivated by Liu and Yu [J. Pure Appl. Math. 33 (4)(2002),...