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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 18
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 4, August 2011
  4. Sum of weighted Lebesgue spaces and nonlinear elliptic equations
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 6, December 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 5, October 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 4, August 2011
Sum of weighted Lebesgue spaces and nonlinear elliptic equations
Well-posedness for a class of fourth order diffusions for image processing
On ground state of spinor Bose–Einstein condensates
Multi-valued solutions to Hessian equations
Global existence of weak solutions for the Navier–Stokes equations with capillarity on the half-line
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 3, June 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 2, April 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 18, Issue 1, February 2011
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Sum of weighted Lebesgue spaces and nonlinear elliptic equations

Content Provider SpringerLink
Author Rolando, Sergio Pisani, Lorenzo Badiale, Mari
Copyright Year 2011
Abstract We study the sum of weighted Lebesgue spaces, by considering an abstract measure space $${(\Omega ,\mathcal{A},\mu)}$$ and investigating the main properties of both the Banach space $$L\left( \Omega \right) =\left\{u_{1}+u_{2}:u_{1} \in L^{q_{1}} \left(\Omega \right),u_{2} \in L^{q_{2}} \left( \Omega \right) \right\}, L^{q_{i}} \left( \Omega \right) :=L^{q_{i}} \left( \Omega ,d\mu \right),$$ and the Nemytskiĭ operator defined on it. Then we apply our general results to prove existence and multiplicity of solutions to a class of nonlinear p-Laplacian equations of the form $$-\triangle _{p}u+V\left( \left| x\right| \right) \left| u\right| ^{p-2}u=f\left( \left| x\right| ,u\right) \quad {\rm in} \mathbb{R}^{N}$$ where V is a nonnegative measurable potential, possibly singular and vanishing at infinity, and f is a Carathéodory function satisfying a double-power growth condition in u.
Ending Page 405
Page Count 37
Starting Page 369
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 4
Volume Number 18
Language English
Publisher SP Birkhäuser Verlag Basel
Publisher Date 2011-02-19
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Sum of weighted Lebesgue spaces Nemytskiĭ operator Analysis Zero mass case Quasilinear elliptic equations Nonlinear elliptic equations Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Compact embeddings
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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