On Nirenberg's problem and related topics

Solitons in Field Theory and Nonlinear Analysis

“…The crucial part is to show that the Lagrangian multipliers will give rise to the correct values of the coefficients in the equations to be solved. This situation is similar to that in the prescribed Gaussian curvature problem [17,21,35,73,76,140,164,165,191,220]. Then we prove the existence of a solution by showing that the constrained minimization problem indeed has a solution.…”

Selfdual Maxwell-Chern-Simons Vortices

“…in [5], [16], [19], [34], [40], [41], [47], [48], [52], [60], [63], [69], [70], [85], [91], [92], [95], [96], [102], [103], [104], [105], [107], [114], [115], [135], [136], [134] and [140]). Many of those results were motivated by various other sources of applications beside the ones already mentioned, as discussed for instance, in [12], [29], [51], [79] and [94].…”

Multi-bump solutions and multi-tower solutions for equations onRN

“…It is known that C ∞ scalar curvature functions are dense in C 1,α (0 < α < 1) norms among positive functions, and, in some cases, there exist multiple conformal metrics with the same scalar curvature function; see, for example, [26,27,29,34]. Theorem 1.3 is a different kind of result from those in [26,27,29,34] and it reveals a phenomenon which has not been observed before. We shall use variational reduction method to prove the main results.…”