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Journal of Differential Equations, ISSN 0022-0396, 08/2019, Volume 267, Issue 4, pp. 2503 - 2530
This paper deals with the following prescribed scalar curvature problem−Δu=Q(|y′|,y″)uN+2N−2,u>0,y=(y′,y″)∈R2×RN−2, where Q(y) is nonnegative and bounded. By... 
MATHEMATICS | R-N | CRITICAL EXPONENT | S-N | DELTA-U | EQUATION | CONJECTURE
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 03/2012, Volume 262, Issue 6, pp. 2861 - 2902
In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev... 
Infinitely many solutions | p-Laplacian equations | Critical Sobolev growth | P-Laplacian equations | EXISTENCE | TOPOLOGY | MATHEMATICS | LINKING | MULTIPLICITY | POSITIVE SOLUTIONS
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2014, Volume 16, Issue 4, pp. 1350048 - 1-1350048-16
We study the following singular elliptic equation $$-{\rm div}(|x|^{-2a}\nabla u)-\mu \frac{u}{|x|^{2(1+a)}}=\frac{|u|^{p-2}u}{|x|^{bp}}+\lambda... 
Nehari manifold | singularity | least energy | sign-changing solutions | EXISTENCE | MATHEMATICS, APPLIED | NONEXISTENCE | MULTIPLICITY | MATHEMATICS | NODAL SOLUTIONS | HARDY INEQUALITY | KOHN-NIRENBERG INEQUALITIES | CRITICAL SOBOLEV EXPONENTS | Manifolds | Variational methods | Mathematical analysis | Inequalities | Dirichlet problem | Texts | Boundary conditions
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2015, Volume 54, Issue 1, pp. 163 - 182
Journal Article
Journal d'Analyse Mathématique, ISSN 0021-7670, 3/2019, Volume 137, Issue 1, pp. 231 - 249
We study the following elliptic system with critical exponent: $$\left\{ {\begin{array}{*{20}{c}} { - \Delta u = {\lambda _1}u + {u_1}|u{|^{2*-2}}u + \beta... 
Abstract Harmonic Analysis | Mathematics | Functional Analysis | Dynamical Systems and Ergodic Theory | Analysis | Partial Differential Equations | MATHEMATICS | SOLITONS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2016, Volume 260, Issue 1, pp. 370 - 400
In this paper we study the following Hénon-like equation{−Δu=||y|−2|αup,u>0,inΩ,u=0,on∂Ω, where α>0, p=N+2N−2, Ω={y∈RN:1<|y|<3}, N≥4. We show that for α>0 the... 
Double-boundary-peak solutions | Reduction method | Hénon-like equation | MATHEMATICS | PROFILE | GROUND-STATE SOLUTIONS | Henon-like equation | ASYMPTOTIC-BEHAVIOR
Journal Article
Advances in Differential Equations, ISSN 1079-9389, 2017, Volume 22, Issue 11-12, pp. 867 - 892
In this paper, we study the following fractional nonlinear Schrodinger system { (-Delta)(s)u+ u = mu(1)vertical bar u vertical bar(2p-2)u + beta vertical bar v... 
LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | BENJAMIN-ONO-EQUATION | SOLITARY WAVES | DECAY | POTENTIALS | NONLINEAR SCHRODINGER-EQUATION | UNIQUENESS
Journal Article
Cold Regions Science and Technology, ISSN 0165-232X, 10/2017, Volume 142, pp. 118 - 131
Journal Article
Advances in Mathematics, ISSN 0001-8708, 01/2015, Volume 270, pp. 263 - 301
In this paper, we consider the planar vortex patch problem in an incompressible steady flow in a bounded domain Ω of R2. Let k be a positive integer and let κj... 
Steady solutions | Euler equation | Variational method | Semilinear elliptic equations | Vortex patch | EXISTENCE | MATHEMATICS | VORTICES | RINGS | GLOBAL THEORY | Variational Method | PAIRS
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 05/2011, Volume 52, Issue 5
In this paper, we study a kind of nonlinear Schroedinger-Poisson system with a parameter {epsilon}. For any positive integer m, we prove that there exists... 
DIFFERENTIAL EQUATIONS | MATHEMATICAL SOLUTIONS | WAVE EQUATIONS | NONLINEAR PROBLEMS | SCHROEDINGER EQUATION | PARTIAL DIFFERENTIAL EQUATIONS | EQUATIONS | ALGORITHMS | POISSON EQUATION | MATHEMATICAL LOGIC | MATHEMATICAL METHODS AND COMPUTING
Journal Article
Communications in Mathematical Sciences, ISSN 1539-6746, 2011, Volume 9, Issue 3, pp. 859 - 878
Journal Article
Journal of Materials Chemistry A, ISSN 2050-7488, 2017, Volume 5, Issue 18, pp. 8352 - 8359
The technological implementation of superamphiphobic surfaces has been largely hindered by the stability issues caused by surface abrasion, corrosion,... 
WETTABILITY | PARTICLES | ENERGY & FUELS | MATERIALS SCIENCE, MULTIDISCIPLINARY | CHEMISTRY, PHYSICAL | COPOLYMERS | SELF-CLEANING SURFACES | NANOPARTICLES | SPRAY | SEPARATION | NANOCOMPOSITE COATINGS | WATER | TIO2 | Sand | Surface tension | Robustness | Adhesive bonding | Decomposition | Coatings | Titanium dioxide | Silicon dioxide
Journal Article
ISSN 2050-7488, 5/2017, Volume 5, Issue 18, pp. 8352 - 8359
The technological implementation of superamphiphobic surfaces has been largely hindered by the stability issues caused by surface abrasion, corrosion,... 
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2007, Volume 30, Issue 1, pp. 113 - 136
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2018, Volume 264, Issue 6, pp. 4006 - 4035
This paper investigates the existence and asymptotic behavior of nodal solutions to the following gauged nonlinear Schrödinger... 
Nodal solutions | Gauged Schrödinger equation | Asymptotic behavior
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2012, Volume 253, Issue 5, pp. 1376 - 1398
In this paper, we are concerned with the following nonlinear Schrödinger equations with inverse square potential and critical Sobolev... 
Nonlinear Schrödinger equation | Palais–Smale sequence | Positive solutions | Critical Sobolev exponent | Compactness | Palais-Smale sequence | EXISTENCE | INEQUALITIES | Nonlinear Schrodinger equation | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | MOLECULES | MATHEMATICS | ELLIPTIC PROBLEMS | BOUNDARY | BIFURCATION
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 04/2011, Volume 250, Issue 8, pp. 3448 - 3472
Let Ω be a bounded domain in RN (N⩾2), φ a harmonic function in Ω¯. In this paper we study the existence of solutions to the following problem arising in the... 
EXISTENCE | LOCATION | MATHEMATICS | SHAPE | FREE-BOUNDARY PROBLEMS | IDEAL FLUID | RINGS | LEAST-ENERGY SOLUTIONS | SEMILINEAR NEUMANN PROBLEM | 2 DIMENSIONS
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2010, Volume 12, Issue 6, pp. 1069 - 1092
We consider the following nonlinear Schrödinger–Poisson system in ℝ3 $$ \left\{ \begin{array}{@{}l@{\quad}l} -\Delta u+u+K(|y|)\Phi(y)u=Q(|y|)|u|^{p-1}u, &... 
Infinitely many solutions | reduction argument | non-radial solutions | Schrödinger-Poisson system | Schrodinger-Poisson system | HARTREE | MATHEMATICS, APPLIED | SPHERES | MAXWELL EQUATIONS | SEMICLASSICAL STATES | ELLIPTIC EQUATION | MOLECULES | MATHEMATICS | BOUND-STATES | SOLITARY WAVES | ATOMS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2003, Volume 193, Issue 2, pp. 424 - 434
Let Ω⊂ R N be a bounded domain such that 0∈Ω, N⩾7, 2 ∗= 2N N−2 . We obtain existence of sign-changing solutions for the Dirichlet problem − Δu= μu |x| 2 +|u| 2... 
Compactness | Critical Sobolev and Hardy exponents | Sign-changing solutions | EXISTENCE | MATHEMATICS | EXPONENTS | sign-changing solutions | compactness | EQUATIONS | critical Sobolev and Hardy exponents
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2003, Volume 131, Issue 6, pp. 1857 - 1866
Let \Omega \subset R^N be a bounded domain such that 0 \in \Omega, N \geq 3,2^*=\frac{2N}{N-2},\lambda \in R, \epsilon \in R . Let \{u_n\}\subset H_0^1(\Omega)... 
Topological compactness | Boundary value problems | Infinity | Applied mathematics | Critical points | Mathematical constants | Nonlinearity | Mathematical inequalities | Sobolev and Hardy critical exponents | Compactness | Palais-Smale sequence | MATHEMATICS | MATHEMATICS, APPLIED | compactness | BOUNDARY-VALUE-PROBLEMS | NONLINEARITIES
Journal Article
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