DOI:
https://doi.org/10.69717/ijams.v2.i2.142Keywords:
Nonlinear elliptic equations, Leray-Lions operator, Variable exponents, Weak solution, Variational methods, Irregular DataAbstract
This work investigates a class of nonlinear elliptic problems posed on a bounded domain Ω ⊆ RN (N ≥ 2), described by the partial differential equation -div (H(x, ∇Z)) = F, where H is an operator of Leray-Lions type acting from the space W 1,α(·) 0 (A) into its dual.
When the right-hand side F belongs to Lθ(·)(A), with θ(·) > 1 satisfying certain conditions, we prove the existence of weak solutions for this class of problems under α(·)-growth conditions. Our approach is based on a combination of variational methods, approximation techniques, and compactness arguments. The functional framework involves Sobolev spaces with variable exponents, W 1,α(·) 0 (A), as well as Lebesgue spaces with variable exponents, Lα(·)(A).
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