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Journal of Functional Analysis, ISSN 0022-1236, 03/2019, Volume 276, Issue 6, pp. 1806 - 1852
We consider fully nonlinear uniformly elliptic equations with quadratic growth in the gradient, such as−F(x,u,Du,D2u)=λc(x)u+〈M(x)Du,Du〉+h(x) in a bounded... 
A priori bounds | Quadratic growth | Fully nonlinear | Multiplicity | EXISTENCE | MATHEMATICS | VISCOSITY SOLUTIONS | MAXIMUM PRINCIPLE | REGULARITY | ELLIPTIC-EQUATIONS
Journal Article
IMA Journal of Numerical Analysis, ISSN 0272-4979, 10/2019, Volume 39, Issue 4, pp. 2069 - 2095
Abstract By analyzing accelerated proximal gradient methods under a local quadratic growth condition, we show that restarting these algorithms at any frequency... 
MATHEMATICS, APPLIED | restarting | COORDINATE DESCENT METHODS | quadratic growth condition | MINIMIZATION | ALGORITHM | CONVERGENCE | accelerated gradient descent | unknown error bound | PARALLEL | Mathematics - Optimization and Control | Mathematics | Optimization and Control
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 02/2019, Volume 276, Issue 4, pp. 1294 - 1312
In this paper, we study semilinear elliptic systems with critical nonlinearity of the form(0.1)Δu=Q(x,u,∇u), for u:Rn→RK, Q has quadratic growth in ∇u. Our... 
Quadratic growth of gradient | Elliptic systems with critical nonlinearity | Harmonic and biharmonic maps | Lorentz space | MATHEMATICS | HARMONIC MAPS | nonlinearity | Elliptic systems with critical
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2017, Volume 448, Issue 2, pp. 1120 - 1146
In this paper, we deal with the following singular elliptic system:{−Δu+α|∇u|2u=pp+qa(x)|v|q|u|p−2u+f,x∈RN,−Δv+β|∇v|2v=qp+qa(x)|u|p|v|q−2v+g,x∈RN, where N≥3,... 
Singular elliptic systems | Sub-supersolutions | Concentration-compactness principle | Quadratic growth in the gradient | Variational method | Nehari manifold | EXISTENCE | MATHEMATICS, APPLIED | NONEXISTENCE | QUASI-LINEAR EQUATIONS | CONVECTION TERM | MATHEMATICS | SYMMETRY | POSITIVE ENTIRE SOLUTIONS | DOMAINS
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 04/2015, Volume 268, Issue 8, pp. 2298 - 2335
We consider the boundary value problem(Pλ)u∈H01(Ω)∩L∞(Ω):−Δu=λc(x)u+μ(x)|∇u|2+h(x), where Ω⊂RN, N≥3 is a bounded domain with smooth boundary. It is assumed... 
Quadratic growth in the gradient | Topological degree | Continuum of solutions | Elliptic equations | EXISTENCE | MATHEMATICS | Topological | QUADRATIC GROWTH | EQUATIONS | UNIQUENESS | Analysis of PDEs | Mathematics
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 12/2019, Volume 132, pp. 308 - 333
Let Ω⊂RN, N≥2, be a smooth bounded domain. We consider a boundary value problem of the form−Δu=cλ(x)u+μ(x)|∇u|2+h(x),u∈H01(Ω)∩L∞(Ω) where cλ depends on a... 
A priori bound | p-Laplacian | Critical growth in the gradient | Boundary weak Harnack inequality | Continuum of solutions | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | QUADRATIC GROWTH | EQUATIONS | UNIQUENESS | Analysis of PDEs | Mathematics
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 05/2017, Volume 262, Issue 10, pp. 5231 - 5270
We consider the boundary value problem(Pλ)−Δu=λc(x)u+μ(x)|∇u|2+h(x),u∈H01(Ω)∩L∞(Ω), where Ω⊂RN,N≥3 is a bounded domain with smooth boundary. It is assumed that... 
Lower and upper solutions | Quasilinear elliptic equations | Quadratic growth in the gradient | MATHEMATICS | MAXIMUM PRINCIPLE | QUADRATIC GROWTH | EQUATIONS | UNIQUENESS | Analysis of PDEs | Mathematics
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2015, Volume 53, Issue 1, pp. 185 - 212
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2014, Volume 256, Issue 2, pp. 577 - 608
In this paper we consider the problem{u∈W01,p(Ω),−diva(x,u,Du)+b(x,u,Du)=h(x,u,Du)in D′(Ω), where −diva(x,u,Du) is a Leray–Lions operator which is defined on... 
Existence | Nonlinear elliptic equations | MATHEMATICS | BOUNDED SOLUTIONS | EXISTENCE RESULT | QUADRATIC GROWTH | Analysis of PDEs | Mathematics
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 02/2013, Volume 38, Issue 2, pp. 244 - 264
Journal Article
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, ISSN 0362-546X, 07/2015, Volume 121, pp. 412 - 423
Journal Article
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, ISSN 1078-0947, 05/2019, Volume 39, Issue 5, pp. 2637 - 2659
In this paper, we establish the existence of a positive solution to {-M lambda,Lambda(+)(D(2)u) + H (x, Du) = K(x)f(u)/u(alpha) in Omega, u > 0 in Omega, u = 0... 
EXISTENCE | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | NONEXISTENCE | CONVECTION | PRINCIPAL EIGENVALUES | MATHEMATICS | ELLIPTIC PROBLEMS | viscosity solution | Pucci's extremal operator | positive solution | singular and gradient nonlinearity | QUADRATIC GROWTH | DIRICHLET PROBLEM | BIFURCATION
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 350, Issue 1, pp. 401 - 408
Given a bounded domain Ω in R N , and a function a ∈ L q ( Ω ) with q > N / 2 , we study the existence of a positive solution for the quasilinear problem − Δ w... 
Singular quasilinear elliptic equations | Positive solutions | Quadratic growth in the gradient | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR ELLIPTIC-EQUATIONS | NATURAL GROWTH | TERMS
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 10/2014, Volume 21, Issue 5, pp. 737 - 749
In this paper, we deal with the following sublinear elliptic system: $${{\left\{\begin{array}{ll}-\Delta u + u + |\nabla u|^2 = a(x)|v|^p+ f,\quad x \in... 
Nonnegative solutions | 35J60 | Analysis | Mathematics | Quadratic growth in the gradient | Sublinear elliptic systems | 35J55 | MATHEMATICS, APPLIED | NONEXISTENCE | SYMMETRY | POSITIVE ENTIRE SOLUTIONS | EQUATIONS | CONVECTION TERM | UNIQUENESS
Journal Article
数学物理学报:B辑英文版, ISSN 0252-9602, 2015, Volume 35, Issue 5, pp. 1023 - 1036
In this article, we consider existence and nonexistence of solutions to problem {-△pu+g(x,u)|↓△|^p=f in -Ω,u=0 on Ω with 1〈p〈∞ where f is a positive measurable... 
解的存在性 | 梯度 | 开集 | 非线性椭圆型方程 | 有界 | 35D05 | quasilinear elliptic equations | existence and nonexistence | 35D10 | 35J92 | 46E30 | gradient terms | singular weights | Existence and nonexistence | Singular weights | Quasilinear elliptic equations | Gradient terms | EXISTENCE | MATHEMATICS | P-GROWTH | QUADRATIC GROWTH | QUASI-LINEAR EQUATIONS | NATURAL GROWTH TERMS
Journal Article
ESAIM: Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 7/2008, Volume 14, Issue 3, pp. 411 - 426
We present a revisited form of a result proved in [Boccardo, Murat and Puel, Portugaliae Math. 41 ( 1982) 507-534] and then we adapt the new proof in order to... 
Singular lower order term | Quadratic gradient | EXISTENCE | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | NONLINEAR ELLIPTIC-EQUATIONS | NATURAL GROWTH TERMS | BOUNDED SOLUTIONS | quadratic gradient | singular lower order term | AUTOMATION & CONTROL SYSTEMS
Journal Article
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, ISSN 1120-6330, 2016, Volume 27, Issue 2, pp. 195 - 233
Journal Article
Asian Journal of Mathematics, ISSN 1093-6106, 2015, Volume 19, Issue 5, pp. 933 - 950
We study the geometry at infinity of expanding gradient Ricci solitons (M-n, g, del f), n >= 3, with finite asymptotic curvature ratio without curvature sign... 
Asymptotic cone | Ricci flow | Expanding gradient ricci soliton | MATHEMATICS | VOLUME GROWTH | MATHEMATICS, APPLIED | expanding gradient Ricci soliton | asymptotic cone | QUADRATIC CURVATURE DECAY | CONVERGENCE | NONNEGATIVELY CURVED MANIFOLDS | FLOW | RIEMANNIAN-MANIFOLDS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2014, Volume 420, Issue 1, pp. 772 - 780
In this note we present some uniqueness and comparison results for a class of problem of the form(0.1)−Lu=H(x,u,∇u)+h(x),u∈H01(Ω)∩L∞(Ω), where Ω⊂RN, N≥2 is a... 
Uniqueness of solution | Quasilinear elliptic equations | Quadratic growth in the gradient | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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