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

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

GLOBAL STRUCTURE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SECOND ORDER m-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the nonlinear eigenvalue problems u′′ + λh(t)f(u) = 0, 0 < t < 1, u(0) = 0, u(1) = m−2 X

Multiple Positive Solutions for Nonlinear Second-order M-point Boundary-value Problems with Sign Changing Nonlinearities

In this paper, we study the nonlinear second-order m-point boundary value problem u′′(t) + f(t, u) = 0, 0 ≤ t ≤ 1, βu(0)− γu′(0) = 0, u(1) = m−2 X i=1 αiu(ξi), where the nonlinear term f is allowed to change sign. We impose growth conditions on f which yield the existence of at least two positive solutions by using a fixed-point theorem in double cones. Moreover, the associated Green’s function...

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