We study the sum of weighted Lebesgue spaces, by considering an abstract measure space (Ω,A, μ) and investigating the main properties of both the Banach space L(Ω) = {u1 + u2 : u1 ∈ Lq1 (Ω) , u2 ∈ Lq2 (Ω)}, Lqi (Ω) := Lqi (Ω, dμ) , and the Nemytski˘ı 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.
Sum of weighted Lebesgue spaces and nonlinear elliptic equations
BADIALE, Marino;
2011-01-01
Abstract
We study the sum of weighted Lebesgue spaces, by considering an abstract measure space (Ω,A, μ) and investigating the main properties of both the Banach space L(Ω) = {u1 + u2 : u1 ∈ Lq1 (Ω) , u2 ∈ Lq2 (Ω)}, Lqi (Ω) := Lqi (Ω, dμ) , and the Nemytski˘ı 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.
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