Infinitely many nonradial solutions of a euclidean scalar field equation - Bartsch, Thomas; Willem, Michel (Journal of functional analysis, 1993)
We study the equation −Δu + b(|x|) u = ƒ(|x|, u), x ∈ RN;u ∈ H1(RN). The existence of a nonradial solution has been an open problem for some time even in the autonomous case. Under suitable hypotheses mainly on ƒ we find an unbounded sequence of nonradial solutions if N = 4 or N ≥ 6. We also obtain infinitely many solutions if b and ƒ are not rotationally symmetric with respect to x but satisfy only a weaker symmetry.
Elektronische Reproduktion der Druck-Ausgabe 25. Mai 2002
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