We establish the existence of positive multipeak solutions to the nonlinear scalar field equation with zero mass −∆u = f(u), u ∈ D1,2(ΩR), 0 whereΩR :={x∈RN :|u|>R}withR>0,N≥4,andthenonlinearityfis subcritical at infinity and supercritical near the origin. We show that the number of positive multipeak solutions becomes arbitrarily large as R → ∞.
Positive multipeak solutions to a zero mass problem in exterior domains
Benedetta Pellacci
2021
Abstract
We establish the existence of positive multipeak solutions to the nonlinear scalar field equation with zero mass −∆u = f(u), u ∈ D1,2(ΩR), 0 whereΩR :={x∈RN :|u|>R}withR>0,N≥4,andthenonlinearityfis subcritical at infinity and supercritical near the origin. We show that the number of positive multipeak solutions becomes arbitrarily large as R → ∞.File in questo prodotto:
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