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math.AP2015★ 1 cited
Compactness results for the -Laplace equation
Marino Badiale, Michela Guida, Sergio Rolando
Given and two measurable functions and , , we define the weighted spaces \[ W=\left\{ u\in D^{1,p}(\mathbb{R}^N):\int_{\mathbb{R}^N}V\left(\left|x…
math.AP2015★ 15 cited
Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence
Marino Badiale, Michela Guida, Sergio Rolando
We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation \[ -\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right|…