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Existence of solution for a singular fractional Laplacian problem with variable exponents and indefinite weights
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2020-04-27 , DOI: 10.1080/17476933.2020.1756270 R. Chammem 1 , A. Ghanmi 1 , A. Sahbani 1
中文翻译:
具有可变指数和不定权重的奇异分数式拉普拉斯问题的解的存在性
更新日期:2020-04-27
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2020-04-27 , DOI: 10.1080/17476933.2020.1756270 R. Chammem 1 , A. Ghanmi 1 , A. Sahbani 1
Affiliation
In this paper, we consider a class of fractional Laplacian problems of the form: where is a bounded domain and is the fractional -Laplacian. We assume that λ is a nonnegative parameter and is a continuous function. By using variational methods and monotonicity arguments combined with the theory of the generalized Lebesgue Sobolev spaces, we prove the existence of solutions to problem .
中文翻译:
具有可变指数和不定权重的奇异分数式拉普拉斯问题的解的存在性
在本文中,我们考虑以下形式的一类分数拉普拉斯问题: 在哪里 是一个有界域并且 是小数 - 拉普拉斯。我们假设λ是一个非负参数,并且是连续函数。通过使用变分方法和单调性论证,结合广义 Lebesgue Sobolev 空间的理论,我们证明了问题的解的存在性.