24 citations · 134 across the 80 of their papers we have counts for
83 papers
A new class of nonlocal operators: the fractional logarithmic -Laplacian and its properties
Anouar Bahrouni, Abdelhamid Gouasmia, Hichem Hajaiej +1
In this paper, we introduce and investigate the fractional logarithmic -Laplacian , defined as the first-order derivative with respect to the parameter of…
The best constant in the G-N inequality for the mixed local and Nonlocal Laplacian
Hichem Hajaiej, Yu Su
In this paper, we establish the best constant in the G-N inequality for the mixed local and nonlocal Laplacian. In our problem, classical methods cannot apply directly since regula…
Local Existence, Uniqueness, Regularity, and Global Behavior of Evolution Equations Involving Mixed Local and Nonlocal Operators
Abdelhamid Gouasmia, Hichem Hajaiej, Kaushik Bal
In this work, we address a parabolic problem featuring a potentially doubly nonlinear term, governed by a combination of local and nonlocal operators (see Problem P1 below). We fir…
The role of the mean curvature in nonlinear p-Laplacian problems with critical exponent
Hichem Chtioui, Hichem Hajaiej, Lovelesh Sharma
We deal with critical nonlinear problems involving the p-Laplacian operator on bounded domains with mixed boundary conditions. We prove the existence of least energy solutions. Our…
Existence of positive and sign-changing solutions for a Choquard equation involving mixed local and nonlocal operators
Shaoxiong Chen, Hichem Hajaiej, Min Yang +1
We study the Choquard equation involving mixed local and nonlocal operators \[ -Δu + (-Δ)^{s}u + V(x)u = \left(\frac{1}{|x|^μ} * F(u)\right) f(u) \quad \text{in } \mathbb{R}^{2}, \…
Lower and Upper Bounds for Sums of Eigenvalues of the Fractional-Logarithmic Laplacian
Maha Daoud, Hichem Hajaiej
In this work, we establish lower and upper bounds for sums of the Dirichlet eigenvalues of the fractional-logarithmic Laplacian. A main challenge in such a study comes from the fac…