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Minimax Theory and its Applications 04 (2019), No. 1, 189--204
Copyright Heldermann Verlag 2019

Multiple Nonradial Solutions for a Nonlinear Elliptic Radial Problem: an Improved Result

Sergio Rolando
Dip. di Matematica e Applicazioni, UniversitÓ di Milano Bicocca, Via Cozzi 53, 20125 Milano, Italy


We obtain an improved version of a recent result concerning the existence of nonnegative nonradial solutions $u\in D^{1,2}(\mathbb{R}^{N})\cap L^{2}(% \mathbb{R}^{N},\left| x\right| ^{-\alpha }dx)$ to the equation \[\smash{ -\triangle u+\displaystyle\frac{A}{\left| x\right| ^{\alpha }\vrule width0pt height10pt depth0pt}u = f\left( u\right) \quad \text{in }\mathbb{R}^{N},\quad N\geq 3,\quad A,\,\alpha >0, } \] where $f$ is a continuous nonlinearity satisfying $f\left( 0\right) =0$.

Keywords: Semilinear elliptic PDE, singular vanishing potential, symmetry breaking.

MSC: 35J60; 35Q55, 35J20.

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