collaborators

15 papers

math.AP2026

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}…

math.AP2026

On the fractional logarithmic -Laplacian

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 o…

math.AP2026

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…

math.AP2026

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…

math.DG2026

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…

math.AP2026

On the lower bound and upper bound of the Sum of Eigenvalues of the Fractional-Logarithmic Laplacian

H. Hajaiej

We establish a lower bound and an upper bound to the sum of the Fractional-Logarithmic Laplacian. A main challenge in such a study comes from the fact that this operator has a Four…