MULTIPLICITY AND CONCENTRATION OF POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS WITH STEEP POTENTIAL

作者：Cheng Yi hsin; Wu Tsung Fang^*

来源：Communications on Pure and Applied Analysis, 2016, 15(6): 2457-2473.

DOI：10.3934/cpaa.2016044

• Semilinear elliptic problems
• concave-convex nonlinearities
• variational methods
• steep potential

In this paper, we study the existence, multiplicity and concentration of positive solutions for the following indefinite semilinear elliptic equations involving concave-convex nonlinearities:
{-Delta u + V-lambda(x) u = (x)vertical bar u vertical bar(q-2) u + g(x)vertical bar u vertical bar(p-2)u in R-N,
u >= 0, in R-N,
where 1 < q < 2 < p < 2* (2* = 2N/N-2 for N >= 3) the potential V-lambda(x) = lambda V+ (x) - V- (x) with V-+/- = max {+/- V, 0} and the parameter lambda > 0. We assume that the functions f,g and V satisfy suitable conditions with the potential V and the weight function g without the assumptions of infinite limits.

• 出版日期2016-11