On positive weak solutions for a class of quasilinear elliptic systems

Existence of positive solutions for variable exponent elliptic systems

“…It arises from nonlinear elasticity theory, electrorheological fluids, etc., (see [1][2][3]). Many results have been obtained on this kind of problems, for example [1,[3][4][5][6][7][8]. In [7], Fan gives the regularity of weak solutions for differential equations with variable exponent.…”

“…Especially, if p(x) ≡ p (a constant), (P) is the well-known p-Laplacian system. There are many articles on the existence of solutions for p-Laplacian elliptic systems, for example [5,10].…”

Three solutions for a class of quasilinear elliptic systems involving the p(x)-Laplace operator

“…For the special case, p(x) ≡ p(a constant), (1.1) becomes the well known p-Laplacian problem. There have been many papers on this class of problems, see [10][11][12][13][14][15][16][17][18][19] and the reference therein.…”

POSITIVE SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN PROBLEMS

“…Especially, if p(x) ≡ p (a constant), (1) is the well-known p-Laplacian systems. There are many papers on the existence of solutions for p-Laplacian elliptic systems, for example, [1][2][3][4][5][6][7][8][9].…”

“…the authors show the existence of positive solutions for problem (2). In this paper, we mainly consider the existence of positive solutions of the system…”