Existence of Solutions to a Class of Semilinear Elliptic Problem with Nonlinear Singular Terms and Variable Exponent

Abstract EN

The authors of this paper prove the existence and regularity results for the homogeneous Dirichlet boundary value problem to the equation - d i v ( M ( x ) ∇ u n ) = f ( x ) / u α ( x ) with f ∈ L m ( Ω ) ( m ⩾ 1 ) and α ( x ) > 0 .

The results show the dependence of the summability of f in some Lebesgue spaces and on the values of α ( x ) .