Second-order ordinary differential equations with indefinite weight: the Neumann boundary value problem

Abstract

We study the second order nonlinear differential equation u ′′ +a(t)g(u) = 0, where g is a continuously differentiable function of constant sign defined on an open interval I ⊆ R and a(t) is a sign-changing weight function. We look for solutions u(t) of the differential equation such that u(t) ∈ I, satisfying the Neumann boundary conditions. Special examples, considered in our model, are the equations with singularity, for I = R Mathematics Subject Classification. 34B15, 34B09.

A Dirichlet problem on the half-line for nonlinear equations with indefinite weight

“…Observe that (5) implies that k 0 , k ∞ ≤ 1. The BVP (1)-(2) is a Dirichlet-type BVP on a unbounded domain.…”

Pairs of positive radial solutions for a Minkowski-curvature Neumann problem with indefinite weight

“…This approach, which looks very natural when dealing with the periodic problem, has the drawback of not being suited for other boundary conditions. In particular, in spite of the well-known strong analogies existing in this setting between the periodic and the Neumann boundary value problem (see, for instance, [9]), the possibility of proving the Neumann counterpart of the result in [6] is not discussed therein.…”

A class of nonlocal indefinite differential systems

“…Remark 4.1 In Theorem 3.1 and Theorem 3.2, we generalize the results of [38][39][40][41][42][43] in three main directions:…”

“…For convenience, we give a corollary of Proposition 2.3 in [40]. If there exists 0 < σ < ξ such that …”

“…Moreover, a class of indefinite problems have attracted the attention of Ma and Han [38], López-Gómez and Tellini [39], Boscaggin and Zanolin [40,41], Sovrano and Zanolin [42], Bravo and Torres [43], Wang and An [44], and Yao [45]. In [38], Ma and Han considered the following boundary value problem:…”