In this paper, we are working with convolutions on the positive half-line, for Lebesgue integrable functions. Six new introduced. Factorization identities these derived, upon use of Fourier sine and cosine transforms Hermite Such allow us to consider systems convolution type equations half-line. Using two different methods, such integral will be analyzed. Conditions their solvability considered...

where Ω ⊂ R is a smooth domain with smooth boundary ∂Ω such that 0 Î Ω, Δpu = div(|∇u|∇u), 1 < p < N, μ < μ̄ = ( N−p p ), l >0, 1 < q < p, sign-changing weight functions f and g are continuous functions on ̄, μ̄ = ( N−p p ) p is the best Hardy constant and p∗ = Np N−p is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the multiplicity of positive solu...

In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system ðEk;lÞ involving critical exponents and sign-changing weight functions. Using Nehari manifold, the system is proved to have at least two nontrivial nonnegative solutions when the pair of the parameters ðk;lÞ belongs to a certain subset of R. 20...

The aim of the presented study is to optimize different classes high-temperature superconducting (HTS) DC cables for improving their performances in a cryo-electric aircraft considering weight, peak temperature during faults, and ratio current passing through each tape critical HTS tapes. These terms were interpreted into three objective functions, multi-objective optimization algorithm known a...