Existence of positive solutions for elliptic systems with nonstandard -growth conditions via sub-supersolution method

Existence and Asymptotic Behavior of Positive Solutions to -Laplacian Equations with Singular Nonlinearities

“…We refer to [1,2], the background of these problems. Many results have been obtained on this kind of problems, for example, [2][3][4][5][6][7][8][9][10][11][12][13]. In [4,7], Fan and Zhao give the regularity of weak solutions for differential equations with nonstandard p(x)-growth conditions.…”

“…In [4,7], Fan and Zhao give the regularity of weak solutions for differential equations with nonstandard p(x)-growth conditions. On the existence of solutions for p(x)-Laplacian problems in bounded domain, we refer to [5,11,12].…”

Existence of Solutions for a Class of Elliptic Systems in Involving the -Laplacian

“…This fact implies some difficulties, as for example, we cannot use the Lagrange multiplier theorem and Morse theorem in a lot of problems involving this operator. In literature, elliptic systems with standard and nonstandard growth conditions have been studied by many authors [23][24][25][26][27][28] , where the nonlinear function F have different and mixed growth conditions and assumptions in each paper.…”

Existence of positive solutions for a class of p(x)-Laplacian systems

“…Especially, if p(x) ≡ p (a constant), (P) is the well-known p-Laplacian system. There are many papers on this class of problems (see [4,5,14,22]). …”

“…Even if the first eigenfunction of p(x)-Laplacian exists, because of the nonhomogeneity of p(x)-Laplacian, the first eigenfunction cannot be used to constructing the subsolution of p(x)-Laplacian problems. In [22], the author discussed the existence of positive solutions of (P), when the problem (P) is radial. In many cases, the radial symmetric conditions are effectively to deal with p(x)-Laplacian problems.…”