Comparison Results for Semilinear Elliptic Equations via Picone-type Identities

Sturmian Comparison Results for Quasilinear Elliptic Equations in R

We obtain Sturmian comparison results for the nonnegative solutions to Dirichlet problems associated with p-Laplacian operators. From Picone-type identities [4, 9], we obtain results comparing solutions of two types of equations. We also present results related to those operators using Piconetype identities.

Anisotropic Picone identities and anisotropic Hardy inequalities

In this paper, we derive an anisotropic Picone identity for the anisotropic Laplacian, which contains some known Picone identities. As applications, a Sturmian comparison principle to the anisotropic elliptic equation and an anisotropic Hardy type inequality are shown.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Nonlinear Picone identities to Pseudo $p$-Laplace operator and applications

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

Sturm-picone Type Theorems for Second-order Nonlinear Elliptic Differential Equations

The aim of this article is to give Sturm-Picone type theorems for the pair of second order nonlinear elliptic differential equations div(p1(x)|∇u|∇u) + q1(x)f1(u) + r1(x)g1(u) = 0, div(p2(x)|∇v|∇v) + q2(x)f2(v) + r2(x)g2(v) = 0, where | · | denotes the Euclidean length and ∇ = ( ∂ ∂x1 , . . . , ∂ ∂xn )T (the superscript T denotes the transpose). Our results include some earlier results and gene...