The integral operator with logarithmic kernel has only one positive eigenvalue

The Convergence of Family of Integral Operators with Positive Kernel

The solving linear one-dimemsional Volterra integral equations of the second kind in reproducing kernel space

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

Indefinite copositive matrices with exactly one positive eigenvalue or exactly one negative eigenvalue

Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out if a matrix with exactly one negative eigenvalue is strictly copositive or not can be formulated ...

Ela Indefinite Copositive Matrices with Exactly One Positive Eigenvalue or Exactly One Negative Eigenvalue

Checking copositivity of a matrix is a co-NP-complete problem. This paper studies copositive matrices with certain spectral properties. It shows that an indefinite matrix with exactly one positive eigenvalue is copositive if and only if the matrix is nonnegative. Moreover, it shows that finding out if a matrix with exactly one negative eigenvalue is strictly copositive or not can be formulated ...

Positive Solutions for Integral Boundary Value Problem with -Laplacian Operator

We consider the existence, multiplicity of positive solutions for the integral boundary value problem with φ-Laplacian φ u′ t ′ f t, u t , u′ t 0, t ∈ 0, 1 , u 0 ∫1 0 u r g r dr, u 1 ∫1 0 u r h r dr, where φ is an odd, increasing homeomorphism from R onto R. We show that it has at least one, two, or three positive solutions under some assumptions by applying fixed point theorems. The interestin...