Abstract:Abstract. Understanding the entire solutions of nonlinear elliptic equations in R N such asis a basic problem in PDE research. This is the context of various classical results in literature like the Gidas-Ni-Nirenberg theorems on radial symmetry, Liouville type theorems, or the achievements around De Giorgi's conjecture.In those results, the geometry of level sets of the solutions turns out to be a posteriori very simple (planes or spheres). On the other hand, problems of the form (0.1) do have solutions with … Show more
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