MULTIPLE POSITIVE SOLUTIONS OF FRACTIONAL ELLIPTIC EQUATIONS INVOLVING CONCAVE AND CONVEX NONLINEARITIES IN RN

作者：Wang, Qingfang^*

来源：Communications on Pure and Applied Analysis, 2016, 15(5): 1671-1688.

DOI：10.3934/cpaa.2016008

• Fractional elliptic equations
• concave and convex
• positive solutions

In this paper, we investigate the existence of positive solutions of the following equation @@@ {(-Delta)(S)v + lambda v = f(x)v(P-1) + h(x)v(q-1), x is an element of R-N, v is an element of H-s(R-N), @@@ where 1 <= q < 2 < p < 2(8)(*) = 2N/N-2s, 0 < s < 1, N > 2s and lambda > 0 is a parameter. Since the concave and convex nonlinearities are involved, the variational functional of the equation has different properties. Via variational method, we show that the equation admits a positive ground state solution for all A > 0 strictly larger than a threshold value. Moreover, under certain conditions on f and for sufficiently large A > 0, we also prove that there are at least k + 1 (k is a positive integer) positive solutions of the equation.

• 出版日期2016-9
• 单位武汉轻工大学