Multipeak solutions for a singularly perturbed Neumann problem

The effect of the graph topology on the existence ofmultipeak solutions for nonlinear Schrödinger equations

“…For example, as a direct corollary of Proposition C.3 and the results in [13,25], we have the following corollary. This paper is arranged as follows.…”

“…The estimates in Appendix C can be used to improve the multiplicity results in [13,25]. For example, as a direct corollary of Proposition C.3 and the results in [13,25], we have the following corollary.…”

The effect of the graph topology on the existence of multipeaksolutions for nonlinear Schrödinger equations

“…The role of the mean curvature function of the boundary ∂Ω in (1.19) is similar to that of the potential V (x) in (1.1). The estimates in Appendix C can be used to improve the multiplicity results in [13,25]. For example, as a direct corollary of Proposition C.3 and the results in [13,25], we have This paper is arranged as follows.…”

Changing-sign bubble solutions for an anisotropic sinh-Poisson equation

“…Next, we have the following result. (15)) is a C 0 -stable critical point for the function F defined in (6). Then, problem (1) has a family of solutions u ε such that as ε → 0,…”

“…Such an idea has been used in many other papers. See for instance [2,[4][5][6][7][11][12][13]18] and references therein. Here we follow those of [21] and introduce an appropriate functional setting, since the distance between the bubbles is small (see Theorem 1.3), but the large extent of μ j bring us some difficulty in the estimates in Sect.…”