Existence and nonexistence of nodal solutions for Choquard type equations with perturbation

[摘要] In this paper, we consider the following Choquard type equations with a local perturbation -Delta u + u = (integral(RN) vertical bar u(y)vertical bar(p)/vertical bar x - y vertical bar(N - alpha) dy)vertical bar u vertical bar(p-2)u + vertical bar u vertical bar(q-2)u in R-N, where N >= 3, alpha is an element of (0, N), q is an element of (2, 2N/N - 2). By employing constrained variational method, gluing approach and Brouwer degree theory, we prove that for any given positive integer k, the above equation with p is an element of (2, N+alpha/N-2) has a least energy radial solution changing sign exactly k times, while when p is an element of (N+alpha/N, 2), the above equation does not admits such a solution. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-15

[关键词] Choquard type equation;Brouwer degree;Gluing approach;Nodal solution;Variational methods