Existence of solutions for critical fractional p-Laplacian equations with indefinite weights
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This article concerns the critical fractional p-Laplacian equation with indefinite weights
(-Δp)su = λg(x)|u|p-2 u + h(x)|u|p*s-2u in ℝN,
where 0 < s < 1 < p < ∞, N > sp and p*s = Np/(N - sp), the weight functions g may be indefinite, and h changes sign. Specifically, based on the results of the asymptotic estimates for an extremal in the fractional Sobolov inequality and the discrete spectrum of fractional p-Laplacian operator, we establish an existence criterion for a nontrivial solution to this problem.
CitationCui, N., & Sun, H. R. (2021). Existence of solutions for critical fractional p-Laplacian equations with indefinite weights. Electronic Journal of Differential Equations, 2021(11), pp. 1-17.
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