Onofri-Type Inequalities for Singular Liouville Equations

Singular Limits in Liouville-type Equations

We consider the boundary value problem ∆u+ε k(x) e = 0 in a bounded, smooth domain Ω in R with homogeneous Dirichlet boundary conditions. Here ε > 0, k(x) is a non-negative, not identically zero function. We find conditions under which there exists a solution uε which blows up at exactly m points as ε→ 0 and satisfies ε ∫ Ω keε → 8mπ. In particular, we find that if k ∈ C(Ω̄), infΩ k > 0 and Ω is...

Hardy Type Inequalities via Riccati and Sturm–Liouville Equations

We discuss integral estimates for domain of solutions to some canonical Riccati and Sturm–Liouville equations on the line. The approach is applied to Hardy and Poincaré type inequalities with weights.

Liouville type theorems and Harnack type inequalities for semilinear elliptic equations

Singular value inequalities for positive semidefinite matrices

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.

The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points

In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.