In this paper, we study the existence of multiple solutions to a Caffarelli- Kohn-Nirenberg type equation with asymptotically linear term at infinity. In this case, the well-known Ambrosetti-Rabinowtz type condition doesn't hold, hence it is difficult to verify the classical (PS) condition. To...

We define a class of formal expansions of a rational function with at least one nonzero pole. To distinct formal expansions and in this class we associate structured arrays and , defined by and where (≠ 0), ,...,, and ,..., are integers and , ..., are nonzero complex constants. We study the...

We find relations between quantities defining geometry and quantities defining the length of a curve in geometries underlying Electromagnetism and unified model of Electromagnetism and Gravitation. And we show that the length of a vector changes along a curve in these geometries

We have computed true star-discrepancies D*(N) for Halton and Niederreiter point sequences in dimensions s = 2, 3, 4, and 6 with N up to 250 000, 10 000, 2000 and 300, respectively. For comparison, we calculated also some L discrepancies T*. The mean behaviour of D*(N) can well be approximated...

Several test functions, whose variation could be calculated, were integrated with up tp 10 trials using different low-discrepancy sequences in dimensions 3, 6, 12, and 24. The errors divided by the variation were compared with exact and asymptotic discrepancies. The errors follow an approximate...

Let ∈ ℂ and ∈ ℂ be nontrivial involutions; i.e., = ≠ ± and = ≠ ±. We say that ∈ ℂ is (, )-symmetric ((, )-skew symmetric) if = ( = −).We give an explicit representation of an arbitrary ()-symmetric matrix in terms of matrices and associated with and and associated with . If =...

Suppose that −∞ < < < ∞, ≤ ≤ ≤ … ≤ ≤ , and ≤ ≤ ≤ … ≤ ≤ , ≥ 1. We simplify and strenghthen Weyl's definition of asymptotic equal distribution of and by showing that the following statements are equivalent:(i) for all ∈ [, ].(ii) .(iii) for all ∈ [, ]

In this paper, using Mountain Pass Lemma and Linking Argument, we prove the existence of nontrivial weak solutions for the Dirichlet problem for the superlinear equation of Caffarelli-Kohn-Nirenberg type in the case where the parameter λ ∈ (0, λ), λ is the second positive eigenvalue of the...