his paper is concerned with the existence and multiplicity of solutions for the fractional variable order Choquard type problem (Formula presented.) where (Formula presented.) and (Formula presented.) are two fractional Laplace operators with variable order (Formula presented.) and with different variable exponents (Formula presented.) and (Formula presented.). Here (Formula presented.) is a bounded smooth domain with at least (Formula presented.), λ is a real parameter, β, μ and k are continuous variable parameters, while F is the primitive function of a suitable f. Under some appropriate conditions on β and k, through variational methods, we prove existence and multiplicity of solutions for the above problem.
Zuo, J., Fiscella, A., Bahrouni, A. (2022). Existence and multiplicity results for p(.)&q(.) fractional Choquard problems with variable order. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 67(2), 500-516 [10.1080/17476933.2020.1835878].
Existence and multiplicity results for p(.)&q(.) fractional Choquard problems with variable order
Fiscella A
;
2022
Abstract
his paper is concerned with the existence and multiplicity of solutions for the fractional variable order Choquard type problem (Formula presented.) where (Formula presented.) and (Formula presented.) are two fractional Laplace operators with variable order (Formula presented.) and with different variable exponents (Formula presented.) and (Formula presented.). Here (Formula presented.) is a bounded smooth domain with at least (Formula presented.), λ is a real parameter, β, μ and k are continuous variable parameters, while F is the primitive function of a suitable f. Under some appropriate conditions on β and k, through variational methods, we prove existence and multiplicity of solutions for the above problem.
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