On singular elliptic equations involving critical Sobolev exponent

Physics and Mathematics of Nonlinear Phenomena 2013

Tahri, K.^1

Preparatory School in Economics, Business and Management Sciences Department of Mathematics, B.P 1085 Bouhannak, Tlemcen, Algeria^1

关键词: Critical sobolev exponent;    Lebesgue space;    Riemannian manifold;    Semilinear elliptic equation;    Singular elliptic equation;    Strong solution;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/482/1/012040/pdf
DOI  :  10.1088/1742-6596/482/1/012040

来源: IOP

【 摘 要 】

Given a n-dimensional compact Riemannian manifold (M, g) with n ≥ 5, we consider the following semi-linear elliptic equation: where the functions a, b and h are in suitable Lebesgue spaces, 20 a real parameter, f is a smooth positive function and the operator Pgis coercive. Under some additional conditions, we obtain results concering the existence of strong solutions of the above equation in H22(M).