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

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

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

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

We consider the existence of multi-peak solutions to two types of free boundary problems arising in confined plasma and steady vortex pair under conditions on...

35J20 | 35J61 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | SEMILINEAR ELLIPTIC PROBLEMS | ASYMPTOTIC SHAPE | PLASMA PROBLEM | STEADY VORTEX RINGS | HOMOCLINIC ORBITS | PAIRS | Mathematical analysis | Vortices | Fluid flow | Nonlinearity | Boundaries | Calculus of variations | Free boundaries | Optimization

35J20 | 35J61 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR SCHRODINGER-EQUATIONS | SEMILINEAR ELLIPTIC PROBLEMS | ASYMPTOTIC SHAPE | PLASMA PROBLEM | STEADY VORTEX RINGS | HOMOCLINIC ORBITS | PAIRS | Mathematical analysis | Vortices | Fluid flow | Nonlinearity | Boundaries | Calculus of variations | Free boundaries | Optimization

Journal Article

25.
Full Text
Sign-changing solutions of an elliptic system with critical exponent in dimension N = 5

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

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

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

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

To analyse the damage characteristics of thermosyphon embankments in a permafrost region, the Qingshui River section along the Qinghai-Tibet Highway (QTH) was...

Field observation | Drilling | Embankment | Thermosyphon | Embankment damage | Longitudinal crack | ENGINEERING CORRIDOR | CHINA | PERFORMANCE | CRUDE-OIL PIPELINE | DISTURBANCE | 2-PHASE CLOSED THERMOSIPHON | ENGINEERING, CIVIL | GEOSCIENCES, MULTIDISCIPLINARY | ENGINEERING, ENVIRONMENTAL | PERMAFROST REGIONS | DEGRADATION | FOUNDATION SOILS | IN-SITU | Case studies | Waterfront development | Analysis | Road construction

Field observation | Drilling | Embankment | Thermosyphon | Embankment damage | Longitudinal crack | ENGINEERING CORRIDOR | CHINA | PERFORMANCE | CRUDE-OIL PIPELINE | DISTURBANCE | 2-PHASE CLOSED THERMOSIPHON | ENGINEERING, CIVIL | GEOSCIENCES, MULTIDISCIPLINARY | ENGINEERING, ENVIRONMENTAL | PERMAFROST REGIONS | DEGRADATION | FOUNDATION SOILS | IN-SITU | Case studies | Waterfront development | Analysis | Road construction

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

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

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

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

We investigate elliptic equations related to the Caffarelli–Kohn–Nirenberg inequalities: $${-div(|x|^\alpha |\nabla u|^{p-2}\nabla u)=|x|^\beta...

Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | 35J60 | Mathematical and Computational Physics | Analysis | 35B33 | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | POSITIVE SOLUTIONS | HARDY EXPONENTS | CRITICAL GROWTH | CRITICAL NONLINEARITIES | TERMS | EXTREMAL-FUNCTIONS | CRITICAL SOBOLEV EXPONENTS | PRINCIPLE | COMPACTNESS

Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | 35J60 | Mathematical and Computational Physics | Analysis | 35B33 | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | POSITIVE SOLUTIONS | HARDY EXPONENTS | CRITICAL GROWTH | CRITICAL NONLINEARITIES | TERMS | EXTREMAL-FUNCTIONS | CRITICAL SOBOLEV EXPONENTS | PRINCIPLE | COMPACTNESS

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

Nodal solutions | Gauged Schrödinger equation | Asymptotic behavior

Journal Article

36.
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Solutions of Schrödinger equations with inverse square potential and critical nonlinearity

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

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

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

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

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

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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