Multiple positive solutions of semilinear elliptic equations involving concave and convex nonlinearities in ℝ N

Abstract

In this article, we investigate the effect of the coefficient f(z) of the sub-critical nonlinearity. For sufficiently large l > 0, there are at least k + 1 positive solutions of the semilinear elliptic equationswhere 1 ≤ q < 2 <p < 2* = 2N/(N -2) for N ≥ 3.

Multiple positive solutions of fractional elliptic equations involving concave and convex nonlinearities in $R^N$

“…For λ = 0, f (x) = h(x) ≡ 1, Ambrosetti et al [1] considered equation (1) on bounded domain with concave-convex nonlinearity. In [14], Lin studied the equation with s = 1 has a positive ground stste solution and for λ large enough, the equation admits at least k + 1 positive solutions. For more results of the case s = 1, we refer the readers to the papers [14,27,8,25] and the references therein.…”

“…In particular, by the version given by (2) for (−∆) s , Brarrios et al [3] investigated the fractional Laplace equation involving concave-convex nonlinearity on bounded domain Ω. Any other reference, readers can consider [14,19,21].…”