Jifeng Chu

Multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces

Abstract The existence of multiple positive solutions to superlinear periodic boundary value problems with repulsive singular forces is discussed in this paper. Our nonlinearity may be singular in its dependent variable and our analysis relies on a nonlinear alternative of Leray–Schauder type and on a fixed point theorem in cones.

Multiplicity of positive periodic solutions to second order differential equations

In this paper, we study the existence of positive periodic solutions to the equation x ″ = f ( t, x ). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

In this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

Complete structure of the Fučík spectrum of the p-Laplacian with integrable potentials on an interval

To characterize the complete structure of the Fucik spectrum of the p-Laplacian on higher dimensional domains is a long-standing problem. In this paper, we study the p-Laplacian with integrable potentials on an interval under the Dirichlet or the Neumann boundary conditions. Based on the strong continuity and continuous differentiability of solutions in potentials, we will give a comprehensive characterization of the corresponding Fucik spectra: each of them is composed of two trivial lines and a double-sequence of differentiable, strictly decreasing, hyperbolic-like curves; all asymptotic lines of these spectral curves are precisely described by using eigenvalues of the p-Laplacian with potentials; and moreover, all these spectral curves have strong continuity in potentials, i.e. as potentials vary in the weak topology, these spectral curves are continuously dependent on potentials in a certain sense.

Periodic solutions for second order singular differential systems with parameters

In this paper we consider the existence of periodic solutions of one-parameter and two-parameter families of second order singular differential equations.

Existence for Singular Periodic Problems: A Survey of Recent Results

We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.

Dynamical Aspects of Initial/Boundary Value Problems for Ordinary Differential Equations

Dynamical aspects of initial/boundary value problems for ordinary differential equations have become a rapidly growing area of research in the theory of differential equations and dynamical systems and have gathered substantial research interests during the last decades. The attractiveness of this field not only is derived from theoretical interests but also is motivated by the insights that such dynamical aspects could reveal in several phenomena observed in applied sciences. The current special issue places its emphasis on the study of the dynamical aspects of initial/boundary value problems for ordinary differential equations. Call for papers has been carefully prepared by the guest editors and posted on the journals web page, which has attracted many researchers to submit their contribution on wide topics such as oscillation theory, delay differential equation, impulsive differential equation, multipoint boundary value problems, stochastic mutualism system, chaotic system, homoclinic solutions, Hamiltonian systems, stability and bifurcation, exponential extinction, singular elliptic problem, nonuniform exponential contraction and dichotomy. All manuscripts submitted to this special issue went through a thorough peer-refereeing process. Based on the reviewers’ reports, we collect twenty-five original research articles by more than fifty active international researchers in differential equations and from different countries such as Korea, China, Malaysia, Singapore, Czech Republic, Turkey, Slovenia, India, and USA. Besides, one survey on recent results for the existence of singular periodic problems is also contained. It is certainly impossible to provide in this short editorial note a more comprehensive description for all articles in this special issue. However, the team of the guest editors believes that the results included reflect some recent trends in research and outline new ideas for future studies of dynamical aspects of initial/boundary value problems for ordinary differential equations.

Prevalence of stable periodic solutions in the forced relativistic pendulum equation

We study the prevalence of stable periodic solutions of the forced relativistic pendulum equation for external force which guarantees the existence of periodic solutions. We prove the results for a general planar system.