Proof of the best bounds in Wallis' inequality.
Monotonicity and convexity for the gamma function.
Variational and penalization methods for studying connecting orbits of Hamiltonian systems.
Some properties of Palais-Smale sequences with applications to elliptic boundary-value problems.
Existence and multiplicity results for homoclinic orbits of Hamiltonian systems.
Inequalities for the gamma function.
Notes on double inequalities of Mathieu's series.
Dynamical analysis of DTNN with impulsive effect.
Analysis of crack propagation path on the anisotropic bi-material rock.
On Shafer and Carlson inequalities.
Generalizations of the Ky Fan inequality.
Note on weighted Carleman-type inequality.
A logarithmically completely monotonic function involving the Gamma functions.
Some existence and bifurcation results for solutions of nonlinear Sturm-Liouville eigenvalue problems.
On the average of the sum-of-a-divisors function
We prove an Ω result on the average of the sum of the divisors of n which are relatively coprime to any given integer a. This generalizes the earlier result for a prime proved by Adhikari, Coppola and Mukhopadhyay.
Smoothness for the collision local time of two multidimensional bifractional Brownian motions
Let , be two independent, -dimensional bifractional Brownian motions with respective indices and . Assume . One of the main motivations of this paper is to investigate smoothness of the collision local time where denotes the Dirac delta function. By an elementary method we show that is smooth in the sense of Meyer-Watanabe if and only if .
Maslov index for homoclinic orbits of hamiltonian systems
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