Stability of Solution of a Class of Quasilinear Elliptic Equations

Abstract

In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equations $$ - {\text{div}}\;A_{p} {\left( {x,u} \right)} + a_{p} {\left( {x,u} \right)} = f{\left( x \right)} $$ in space W (θ, p)(Ω), which is bigger than W (1, p)(Ω). Next, using revise reverse Holder inequality we prove that if ω c is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈ U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.