Abstract.We study a second order scalar equation of the form x′′ + V′(x) = p(t), where p is a π-perodic function and V is a singular potential. We give sufficient conditions on V, p ensuring that all… Expand

In this paper we are concerned with the existence and multiplicity of radial solutions to the BVP whereB is an open ball in ℝK and u↦∇·(a(|∇u|)∇u) is a nonlinear differential operator (e.g. the… Expand

We deal with the singularly perturbed Nagumo-type equation where is a real parameter and is a piecewise constant function satisfying 0 < a(s) < 1 for all s. For small e, we prove the existence of… Expand

Given a smooth function $U(t,x)$, $T$-periodic in the first variable and satisfying $U(t,x) = \mathcal{O}(\vert x \vert^{\alpha})$ for some $\alpha \in (0,2)$ as $\vert x \vert \to \infty$, we prove… Expand

Abstract In this paper we are concerned with a differential equation of the form x +c x +q(t)g(x)=0, t∈(a,b), where −∞⩽ a b ⩽+∞, q has infinitely many zeros in ( a , b ), and g is superlinear. We… Expand