Spectrum of Discrete Second-Order Difference Operator with Sign-Changing Weight and Its Applications

Subharmonic solutions and homoclinic orbits of second order discrete Hamiltonian systems with potential changing sign

Sign-Changing Solutions for Discrete Second-Order Three-Point Boundary Value Problems

Multiplicity of Positive Solutions of laplacian systems with sign-changing weight functions

In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.

Spectral Theory from the Second-Order q-Difference Operator

Spectral theory from the second-order q-difference operator Δ q is developed. We give an integral representation of its inverse, and the resolvent operator is obtained. As application , we give an analogue of the Poincare inequality. We introduce the Zeta function for the operator Δ q and we formulate some of its properties. In the end, we obtain the spectral measure. 1. Basic definitions Consi...

Maximum and antimaximum principles for a second order differential operator with variable coefficients of indefinite sign

New criteria for the existence of a maximum or antimaximum principle of a general second order operator with periodic conditions, as well as conditions for nonresonance, are provided and compared with the related literature. The purpose of this paper is to study some qualitative properties of the second order linear operator L½p; qŠu u 00 þ pðtÞu 0 þ qðtÞu with periodic conditions, where p, q 2...