Existence of solutions for a quasilinear elliptic system with local nonlinearity on ℝN

Existence of at least three weak solutions for a quasilinear elliptic system

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

Existence of Positive Solutions of a Class of Quasilinear Elliptic Equations on Rn

In this paper we study the following problem: −Δpu + |u|p−2u = k(x) f (u) + h(x) , x ∈ RN , where u ∈W 1,p(RN) , u > 0 in RN . Under appropriate assumptions on k , h and f , we prove that problem has at least two positive solutions.

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in RN

Correspondence should be addressed to Tsing-San Hsu, [email protected] Received 9 October 2009; Accepted 12 February 2010 Academic Editor: Kanishka Perera Copyright q 2010 Tsing-San Hsu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properl...

Multiple Solutions of Quasilinear Elliptic Equations in RN