arXiv subjects

Hichem Chtioui

Publications and source records attributed to Hichem Chtioui.

8 recordsLinked to original sources

arXiv2026

The role of the mean curvature in nonlinear p-Laplacian problems with critical exponent

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 work shows a significant difference between the semi-linear case p = 2 and the quasilinear case for the existence results. Moreover, neither the results for the Laplacian can be extended to the p-Laplacian, nor the method for the p-Laplacian can apply to the Laplacian setting. Additionally, the cases (p < 2 and p > 2) present different challenges and need to be studied separately. More precisely, when p > 2, the effect of the geometry of the boundary conditions dominates that one of the potential, whereas for p < 2 the opposite behavior holds true.

math.DG↗

arXiv2026

The effect of boundary geometry in nonlocal critical problems with Hardy-Littlewood-Sobolev exponent

In this paper we consider a mixed Dirichlet-Neumann boundary value problem. lem involving Choquard nonlinearity with upper critical exponent in the sense of Hardy- Littlewood Sobolev inequality. We investigate the effect of the geometry of the boundary part where the Neumann condition is prescribed on the existence problem of ground state solutions.

math.AP↗

arXiv2025

Nonlocal Choquard equations involving critical Hardy-Littlewood-Sobolev exponent: the effect of the topology of the domain

We apply a topological method to prove existence of positive solutions for the nonlineair Choquard equation with upper critical exponent in the sense of Hardy-Littlewood-Sobolev inquality on bounded domains having nontrivial homology group.

math.AP↗

arXiv2020

On the Chen-Lin conjecture for the prescribed scalar curvature problem

We prove a criterion of existence of solutions conjectured by C. C. Chen and C. S. Lin [20] for the prescribed scalar curvature problem on the standard n-dimensional sphere.

math.DG↗

arXiv2017

Q-curvature type problem on bounded domains of R^n

In this paper, we establish compactness and existence results to a Branson-Paneitz type problem on a bounded domain of R^n with Navier boundary condition.

math.AP↗

arXiv2009

Conformal metrics of prescribed scalar curvature on $4-$manifolds: The degree zero case

In this paper, we consider the problem of existence and multiplicity of conformal metrics on a riemannian compact $4-$dimensional manifold $(M^4,g_0)$ with positive scalar curvature. We prove new exitence criterium which provides existence results for a dense subset of positive functions and generalizes Bahri-Coron and Chang-Gursky-Yang Euler-Hopf type criterium. Our argument gives estimates on the Morse index of the solutions and has the advantage to extend known existence results. Moreover it provides, for generic $K$ {\it Morse Inequalities at Infinity}, which give a lower bound on the number of metrics with prescribed scalar curvature in terms of the topological contribution of its "critical points at Infinity" to the difference of topology between the level sets of the associated Euler-Lagrange functional.

math.DG↗

arXiv2003

Prescribed Scalar Curvature with Minimal Boundary Mean Curvature on $S^4_+$

This paper is devoted to the prescribed scalar curvature under minimal boundary mean curvature on the standard four dimensional half sphere. Using topological methods from the theory of critical points at infinity, we prove some existence results. These methods were first introduced by A. Bahri.

math.AP↗

arXiv2003

On a Paneitz Type Equation in Six Dimensional Domains

In this paper we consider a fourth order equation involving the critical Sobolev exponent on a bounded and smooth domain in $\R^6$. Using theory of critical points at infinity, we give some topological conditions on a given function defined on a domain to ensure some existence results.

math.AP↗