The authors derive an analog of the well-known Picone identity but for nonlinear dynamic equations on time scales. As a consequence, they obtain a nonlinear comparison theorem in the spirit of the classical Sturm–Picone comparison theorem. Comparison results yielding the nonoscillation of all solutions of nonlinear equations are also obtained. AMS subject classification: 34C10, 34C15, 39A11.

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...

Picone identity for a class of nonlinear differential equations is established and various qualitative results (such as Wirtinger-type inequality and the existence of zeros of first components of solutions) are obtained with the help of this new formula.

We established a Picone identity for systems of nonlinear partial differential equations of first-order. With the help of this formula, we obtain qualitative results such as an integral inequality of Wirtinger type and the existence of zeros for the first components of solutions in a given bounded domain.

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.

We analyze the asymptotic behavior of eigenvalues nonlinear elliptic problems under Dirichlet boundary conditions and mixed (Dirichlet, Neumann) on domains becoming unbounded. make intensive use Picone identity to overcome nonlinearity complications. Altogether makes proof easier with respect known in linear case. Surprisingly critically differs from case pure for some class problems.

In this article, a Picone-type identity for the weighted p-biharmonic operator is established and comparison results for a class of half-linear partial differential equations of fourth order based on this identity are derived.

A Picone type identity is established for homogeneous differential operators involving the pseudo p-Laplacian with variable exponent p = p(x). Using this identity, it is shown that the classical Sturmian theory extends to the associated partial differential equations.

In the paper a Picone-type identity for half-linear differential equations of second order is derived and Sturmian theory for both forced and unforced halflinear and quasilinear equations based on this identity is developed.