Nodal solutions for a second-order m-point boundary value problem

SPECTRAL PROPERTIES AND NODAL SOLUTIONS FOR SECOND-ORDER, m-POINT, p-LAPLACIAN BOUNDARY VALUE PROBLEMS

We consider the m-point boundary value problem consisting of the equation −φp(u) = f(u), on (0, 1), (1) together with the boundary conditions u(0) = 0, u(1) = m−2 X

SPECTRAL PROPERTIES AND NODAL SOLUTIONS FOR SECOND-ORDER, m-POINT, BOUNDARY VALUE PROBLEMS

We consider the m-point boundary value problem consisting of the equation −u′′ = f(u), on (0, 1), where f : R → R is C1, with f(0) = 0, together with the boundary conditions u(0) = 0, u(1) = m−2 X

Global Structure of Nodal Solutions for Second-Order m-Point Boundary Value Problems with Superlinear Nonlinearities

Existence of Positive Solutions of Nonlinear Second-Order M-Point Boundary Value Problem

Under suitable conditions on f t u , ( ) , the nonlinear second-order m-point boundary value problem ′′ + ( ) = u t f t u t ( ) , ( ) 0 , 0 1 < < t u( ) 0 0 = , u a u i i i m ( ) ( ) 1 1 2 = = − ∑ x has at least one positive solution. In this paper, the authors examine the positive solutions of nonlinear second-order m-point boundary value problem. Ma, 2001; Sun, 2005) for some recent results o...

Twin positive solutions of second-order m-point boundary value problem with sign changing nonlinearities

In this paper, we study second-order m-point boundary value problem { u′′(t) + a(t)u′(t) + f(t, u) = 0, 0 ≤ t ≤ 1, u′(0) = 0, u(1) = ∑k i=1 aiu(ξi)− ∑m−2 i=k+1 aiu(ξi), where ai > 0(i = 1, 2, · · ·m − 2), 0 < ∑k i=1 ai − ∑m−2 i=k+1 ai < 1, 0 < ξ1 < ξ2 < · · · < ξm−2 < 1, a ∈ C([0, 1], (−∞, 0)) and f is allowed to change sign. We show that there exist two positive solutions by using Leggett-Will...