Picone-type inequalities for nonlinear elliptic equations with first-order terms and their applications

Pohozaev-type inequalities and their applications for elliptic equations

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...

Comparison Results for Semilinear Elliptic Equations via Picone-type Identities

By means of a Picone’s type identity, we prove uniqueness and oscillation of solutions to an elliptic semilinear equation with Dirichlet boundary conditions.

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

Adaptive Wavelet Methods for Elliptic Operator Equations with Nonlinear Terms

We present an adaptive wavelet method for the numerical solution of elliptic operator equations with nonlinear terms. This method is developed based on tree approximations for the solution of the equations and adaptive fast reconstruction of nonlinear functionals of wavelet expansions. We introduce a constructive greedy scheme for the construction of such tree approximations. Adaptive strategie...