Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 6, pp. 2201 - 2209

We establish coincidence fixed point and common fixed point theorems for mappings satisfying ( ψ , φ ) -weakly contractive condition in an ordered complete...

Weakly contractive condition | Partially ordered set | Common fixed point | Weakly increasing mappings | Coincidence point | Altering distance function | Fixed point | EXISTENCE | MATHEMATICS, APPLIED | PRINCIPLE | UNIQUENESS | MATHEMATICS | MAPS | THEOREMS | SETS | OPERATORS | Nonlinearity | Theorems | Fixed points (mathematics) | Mapping | Metric space

Weakly contractive condition | Partially ordered set | Common fixed point | Weakly increasing mappings | Coincidence point | Altering distance function | Fixed point | EXISTENCE | MATHEMATICS, APPLIED | PRINCIPLE | UNIQUENESS | MATHEMATICS | MAPS | THEOREMS | SETS | OPERATORS | Nonlinearity | Theorems | Fixed points (mathematics) | Mapping | Metric space

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2014, Volume 366, Issue 9, pp. 4919 - 4937

We consider a nonlinear elliptic equation driven by the sum of a p-Laplacian, where 1

Morse theory | Integers | Mathematical theorems | Infinity | Mathematical growth | Critical points | Elliptic equations | Mountain passes | Abstracting | Nontrivial solutions | EXISTENCE | MATHEMATICS | Morse relation | nonlinear regularity | critical groups | strong deformation retract | GROWTH | EQUATIONS | Superlinear reaction | Ambrosetti-Rabinowitz condition

Journal Article

Advances in Mathematics, ISSN 0001-8708, 02/2020, Volume 361, p. 106912

Given a closed Riemannian manifold (M,gM) of dimension n≥3, we prove the existence of a conformally compact Einstein metric g+ defined on a collar neighborhood...

Conformally compact | Local existence | Einstein metric | MATHEMATICS

Conformally compact | Local existence | Einstein metric | MATHEMATICS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2018, Volume 457, Issue 1, pp. 134 - 152

In this paper we consider a nonlinear viscoelastic equation with minimal conditions on the L1(0,∞) relaxation function g namely g′(t)≤−ξ(t)H(g(t)), where H is...

General decay | Convexity | Relaxation function | Viscoelastic damping | 2ND-ORDER EVOLUTION-EQUATIONS | MATHEMATICS, APPLIED | ENERGY | GLOBAL EXISTENCE | STABILITY | UNIFORM DECAY | LINEAR VISCOELASTICITY | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | VOLTERRA EQUATION | MEMORY | DISSIPATIVE SYSTEMS

General decay | Convexity | Relaxation function | Viscoelastic damping | 2ND-ORDER EVOLUTION-EQUATIONS | MATHEMATICS, APPLIED | ENERGY | GLOBAL EXISTENCE | STABILITY | UNIFORM DECAY | LINEAR VISCOELASTICITY | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | VOLTERRA EQUATION | MEMORY | DISSIPATIVE SYSTEMS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 05/2012, Volume 53, Issue 5, pp. 053702 - 053702-14

In this paper, we consider a viscoelastic equation and establish an explicit and general decay rate result without imposing restrictive assumptions on the...

EXISTENCE | ENERGY | VOLTERRA EQUATION | DECAY | MEMORY | BEHAVIOR | SYSTEMS | ASYMPTOTIC STABILITY | PHYSICS, MATHEMATICAL

EXISTENCE | ENERGY | VOLTERRA EQUATION | DECAY | MEMORY | BEHAVIOR | SYSTEMS | ASYMPTOTIC STABILITY | PHYSICS, MATHEMATICAL

Journal Article

Numerical Algorithms, ISSN 1017-1398, 9/2017, Volume 76, Issue 1, pp. 259 - 282

Our aim in this paper is to study strong convergence results for L-Lipschitz continuous monotone variational inequality but L is unknown using a combination of...

Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Subgradient extragradient method | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | 47H09 | 47J05 | 47J25 | 47H06 | Variational inequalities | EXISTENCE | HILBERT-SPACES | MATHEMATICS, APPLIED | HAMMERSTEIN TYPE | HYBRID METHOD | NONLINEAR INTEGRAL-EQUATIONS | BANACH-SPACES | GRADIENT-METHOD | ITERATIVE APPROXIMATION | OPERATORS

Strong convergence | Numeric Computing | Hilbert spaces | Theory of Computation | Subgradient extragradient method | Algorithms | Algebra | Numerical Analysis | Viscosity method | Computer Science | 47H09 | 47J05 | 47J25 | 47H06 | Variational inequalities | EXISTENCE | HILBERT-SPACES | MATHEMATICS, APPLIED | HAMMERSTEIN TYPE | HYBRID METHOD | NONLINEAR INTEGRAL-EQUATIONS | BANACH-SPACES | GRADIENT-METHOD | ITERATIVE APPROXIMATION | OPERATORS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 11

In this paper, we introduce a new type of a generalized- -Meir-Keeler contractive mapping and establish some interesting theorems on the existence of fixed...

generalized -Meir-Keeler contractive mapping | α -admissible mapping | Analysis | Mathematics, general | binary relation | Mathematics | Applications of Mathematics | Generalized (α,φ)- Meir-Keeler contractive mapping | α-admissible mapping | Binary relation | alpha-admissible mapping | MATHEMATICS | MATHEMATICS, APPLIED | THEOREMS | generalized (alpha, psi)-Meir-Keeler contractive mapping | Theorems | Fixed points (mathematics) | Mapping | Metric space | Existence theorems | Inequalities

generalized -Meir-Keeler contractive mapping | α -admissible mapping | Analysis | Mathematics, general | binary relation | Mathematics | Applications of Mathematics | Generalized (α,φ)- Meir-Keeler contractive mapping | α-admissible mapping | Binary relation | alpha-admissible mapping | MATHEMATICS | MATHEMATICS, APPLIED | THEOREMS | generalized (alpha, psi)-Meir-Keeler contractive mapping | Theorems | Fixed points (mathematics) | Mapping | Metric space | Existence theorems | Inequalities

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 4/2016, Volume 23, Issue 2, pp. 1 - 22

In this work we study the following class of problems in $${\mathbb R^{N}, N > 2s}$$ R N , N > 2 s $$\varepsilon^{2s}(-\Delta)^{s}u + V(z)u = f(u), \,\,\,u(z)...

Morse theory | 58E05 | 74G35 | Ljusternick-Schnirelmann category | 35A15 | Analysis | multiplicity of solutions | Mathematics | Fractional Laplacian | 35S05 | EXISTENCE | MATHEMATICS, APPLIED | NUMBER | POSITIVE SOLUTIONS | QUASI-LINEAR EQUATIONS | LAPLACIAN | ELLIPTIC PROBLEMS | DOMAIN TOPOLOGY | SYSTEMS | RIEMANNIAN MANIFOLD | Cytokinins

Morse theory | 58E05 | 74G35 | Ljusternick-Schnirelmann category | 35A15 | Analysis | multiplicity of solutions | Mathematics | Fractional Laplacian | 35S05 | EXISTENCE | MATHEMATICS, APPLIED | NUMBER | POSITIVE SOLUTIONS | QUASI-LINEAR EQUATIONS | LAPLACIAN | ELLIPTIC PROBLEMS | DOMAIN TOPOLOGY | SYSTEMS | RIEMANNIAN MANIFOLD | Cytokinins

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 04/2016, Volume 39, Issue 6, pp. 1480 - 1492

In this note, a critical point result for differentiable functionals is exploited in order to prove that a suitable class of one‐dimensional fractional...

variational methods | fractional problems | existence results | ORDER | MATHEMATICS, APPLIED | LAPLACE EQUATION | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | OPERATORS | Concretes | Nonlinearity | Critical point | Functionals | Asymptotic properties | Mathematical analysis

variational methods | fractional problems | existence results | ORDER | MATHEMATICS, APPLIED | LAPLACE EQUATION | POSITIVE SOLUTIONS | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | OPERATORS | Concretes | Nonlinearity | Critical point | Functionals | Asymptotic properties | Mathematical analysis

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 09/2016, Volume 59, pp. 24 - 30

In this work, by using the minimax method and some analysis techniques, we obtain the uniqueness of positive solutions for a class of Kirchhoff type problems...

Kirchhoff type problems | Singularity | Uniqueness | Minimax method | EXISTENCE | MATHEMATICS, APPLIED | NONTRIVIAL SOLUTIONS | EQUATIONS | SIGN-CHANGING SOLUTIONS | MULTIPLE POSITIVE SOLUTIONS | Minimax technique | Singularities | Mathematical analysis

Kirchhoff type problems | Singularity | Uniqueness | Minimax method | EXISTENCE | MATHEMATICS, APPLIED | NONTRIVIAL SOLUTIONS | EQUATIONS | SIGN-CHANGING SOLUTIONS | MULTIPLE POSITIVE SOLUTIONS | Minimax technique | Singularities | Mathematical analysis

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 02/2017, Volume 95, Issue 1, pp. 73 - 93

The aim of this paper is to deal with the nonlocal fractional counterpart of the Laplace equation involving critical nonlinearities studied by Brezis and...

49J35 | 35A15 | 47G20 | 35S15 (primary) | 45G05 (secondary) | EXISTENCE | MATHEMATICS | MULTIPLICITY | ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | SOBOLEV

49J35 | 35A15 | 47G20 | 35S15 (primary) | 45G05 (secondary) | EXISTENCE | MATHEMATICS | MULTIPLICITY | ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | SOBOLEV

Journal Article

12.
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A multiplicity result for Chern–Simons–Schrödinger equation with a general nonlinearity

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 12/2015, Volume 22, Issue 6, pp. 1831 - 1850

In this paper we give a multiplicity result for the following Chern–Simons–Schrödinger equation $$-\Delta u + 2q u...

35J20 | Variational methods | Analysis | 81T10 | Chern–Simons gauge field | 35Q55 | General nonlinearities | Mathematics | Radial solutions | Schrödinger equation | MOUNTAIN PASS | EXISTENCE | MATHEMATICS, APPLIED | Schrodinger equation | SCALAR FIELD-EQUATIONS | PLANE | Chern-Simons gauge field | STANDING WAVES

35J20 | Variational methods | Analysis | 81T10 | Chern–Simons gauge field | 35Q55 | General nonlinearities | Mathematics | Radial solutions | Schrödinger equation | MOUNTAIN PASS | EXISTENCE | MATHEMATICS, APPLIED | Schrodinger equation | SCALAR FIELD-EQUATIONS | PLANE | Chern-Simons gauge field | STANDING WAVES

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 02/2020, Volume 79, Issue 4, pp. 1208 - 1221

The current paper considers the boundedness of solutions to the following quasilinear Keller–Segel model (with logistic source)...

Parabolic–parabolic | Nonlinear diffusion | Keller–Segel | Boundedness | SYSTEM | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | CHEMOTAXIS-HAPTOTAXIS MODEL | BEHAVIOR | Parabolic-parabolic | Keller-Segel | TIME BLOW-UP | Smooth boundaries

Parabolic–parabolic | Nonlinear diffusion | Keller–Segel | Boundedness | SYSTEM | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | CHEMOTAXIS-HAPTOTAXIS MODEL | BEHAVIOR | Parabolic-parabolic | Keller-Segel | TIME BLOW-UP | Smooth boundaries

Journal Article

Advances in Calculus of Variations, ISSN 1864-8258, 04/2016, Volume 9, Issue 2, pp. 101 - 125

We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in...

Morse theory | regularity of solutions | 35P15 | 35R11 | Fractional | existence and multiplicity of weak solutions | 35P30 | Laplacian problems | Fractional p-Laplacian problems | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | REGULARITY | DIRICHLET PROBLEM | GUIDE | Game theory | Population biology | Phase transitions | Dynamic tests | Phase transformations | Dynamics | Mathematical analysis | Continuum mechanics | Topology | Calculus of variations

Morse theory | regularity of solutions | 35P15 | 35R11 | Fractional | existence and multiplicity of weak solutions | 35P30 | Laplacian problems | Fractional p-Laplacian problems | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | REGULARITY | DIRICHLET PROBLEM | GUIDE | Game theory | Population biology | Phase transitions | Dynamic tests | Phase transformations | Dynamics | Mathematical analysis | Continuum mechanics | Topology | Calculus of variations

Journal Article

Advances in Calculus of Variations, ISSN 1864-8258, 07/2019, Volume 12, Issue 3, pp. 253 - 275

The paper is concerned with existence of nonnegative solutions of a Schrödinger–Choquard–Kirchhoff-type fractional -equation. As a consequence, the results can...

variational methods | Schrödinger–Choquard–Kirchhoff type | 35R11 | 35A15 | 47G20 | critical exponent | fractional p-Laplacian | Schrödinger-Choquard-Kirchhoff type | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLICITY | Schrodinger-Choquard-Kirchhoff type | Existence theorems | Parameters

variational methods | Schrödinger–Choquard–Kirchhoff type | 35R11 | 35A15 | 47G20 | critical exponent | fractional p-Laplacian | Schrödinger-Choquard-Kirchhoff type | MATHEMATICS | MATHEMATICS, APPLIED | MULTIPLICITY | Schrodinger-Choquard-Kirchhoff type | Existence theorems | Parameters

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 02/2017, Volume 33, pp. 33 - 39

Here we give a self-contained new proof of the existence of singular solutions to a class Dirichlet problem with a singular nonlinearity. These results were...

Biharmonic equation | Existence | Singular solution | MATHEMATICS, APPLIED | ELLIPTIC EQUATION | MODELING ELECTROSTATIC ACTUATION | Dirichlet problem | Nonlinearity

Biharmonic equation | Existence | Singular solution | MATHEMATICS, APPLIED | ELLIPTIC EQUATION | MODELING ELECTROSTATIC ACTUATION | Dirichlet problem | Nonlinearity

Journal Article

17.
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Existence Result to a Parabolic Equation with Quadratic Gradient Term and an L-1 Source

ACTA APPLICANDAE MATHEMATICAE, ISSN 0167-8019, 10/2019, Volume 163, Issue 1, pp. 145 - 156

In this paper, we mainly consider the existence of bounded solutions to nonlinear parabolic problem involving natural growth term and L-1 source. Parabolic...

MATHEMATICS, APPLIED | Parabolic equations | INTERPLAY | GLOBAL EXISTENCE | DEGENERATE | COEFFICIENTS | Natural growth | BOUNDED SOLUTIONS | L-infinity bound | Mathematical analysis | Regularization methods | Regularization

MATHEMATICS, APPLIED | Parabolic equations | INTERPLAY | GLOBAL EXISTENCE | DEGENERATE | COEFFICIENTS | Natural growth | BOUNDED SOLUTIONS | L-infinity bound | Mathematical analysis | Regularization methods | Regularization

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2018, Volume 462, Issue 1, pp. 1 - 25

We consider the following fully parabolic Keller–Segel system with logistic source(KS){ut=Δu−χ∇⋅(u∇v)+au−μu2,x∈Ω,t>0,vt=Δv−v+u,x∈Ω,t>0, over a bounded domain...

Logistic source | Global existence | Chemotaxis | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR CHEMOTAXIS SYSTEM | MODELS | GROWTH | EQUATIONS | DIFFUSION | WEAK SOLUTIONS | TIME BLOW-UP

Logistic source | Global existence | Chemotaxis | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR CHEMOTAXIS SYSTEM | MODELS | GROWTH | EQUATIONS | DIFFUSION | WEAK SOLUTIONS | TIME BLOW-UP

Journal Article