Existence Results for an Nonlinear Variable Exponents Anisotropic Elliptic Problems
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In this paper, we prove the existence of distributional solutions in the anisotropic Sobolev space W^(1,p (·))(Ω) with variable exponents and zero boundary, for a class of variable exponents anisotropic nonlinear elliptic equations having a compound nonlinearity G(x, u) = ∑(i=1 to N) (| f | + | u |)^(p_i(x)-1) on the right-hand side, such that f is in the variable exponents anisotropic Lebesgue space Lp (·) (Ω), where p (·) = (p_1(·), . . . , p_N (·)) ∈ (C(Ω, ]1, +∞[))^N.
Abstract
In this paper, we prove the existence of distributional solutions in the anisotropic Sobolev space W^(1,p (·))(Ω) with variable exponents and zero boundary, for a class of variable exponents anisotropic nonlinear elliptic equations having a compound nonlinearity G(x, u) = ∑(i=1 to N) (| f | + | u |)^(p_i(x)-1) on the right-hand side, such that f is in the variable exponents anisotropic Lebesgue space Lp (·) (Ω), where p (·) = (p_1(·), . . . , p_N (·)) ∈ (C(Ω, ]1, +∞[))^N.
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