Multiple Results for Critical Quasilinear Elliptic Systems Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

作者：Chu Chang Mu^*; Tang Chun Lei

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2013, 36(3): 789-805.

• Quasilinear elliptic systems
• critical Sobolev exponent
• concave-convex nonlinearities
• sign-changing weight functions
• Ekeland's variational principle
• mountain pass theorem

This paper is devoted to study the multiplicity of nontrivial nonnegative or positive solutions to the following systems
{-Delta(p)u = lambda a(1)(x)vertical bar u vertical bar(q-2)u + b(x)F-u(u, v), in Omega,
-Delta(p)v = lambda a(2)(x)vertical bar v vertical bar(q-2)v + b(x)F-v(u, v), in Omega,
u = v = 0, on partial derivative Omega,
where Omega subset of R-N is a bounded domain with smooth boundary partial derivative Omega; 1 < q < p < N, p* = (Np)/(N - p); Delta(p)w = div (vertical bar del w vertical bar(p-2)del w) denotes the p-Laplacian operator; lambda > 0 is a positive parameter; a(i) is an element of L-Theta(Omega)(i = 1, 2) with Theta = p(p* - q) and b is an element of L infinity(Omega) are allowed to change sign; F is an element of C-1 ((R+)(2),R+) is positively homogeneous of degree p*, that is, F(tz) = t(p)* F (z) holds for all z is an element of (R+)(2) and t > 0, here, R+ = [0, +infinity). The multiple results of weak solutions for the above critical quasilinear elliptic systems are obtained by using the Ekeland's variational principle and the mountain pass theorem.

• 出版日期2013
• 单位西南大学