Journal of Mathematical Sciences (United States), ISSN 1072-3374, 12/2018, Volume 235, Issue 3, pp. 243 - 255

We study the existence of solutions of an integro-differential equation in the case of the anomalous diffusion with the negative Laplace operator in a...

Differential equations | LAPLACIAN | MATHEMATICAL SOLUTIONS | INTEGRO-DIFFERENTIAL EQUATIONS | DIFFUSION | MATHEMATICAL METHODS AND COMPUTING

Differential equations | LAPLACIAN | MATHEMATICAL SOLUTIONS | INTEGRO-DIFFERENTIAL EQUATIONS | DIFFUSION | MATHEMATICAL METHODS AND COMPUTING

Journal Article

Journal of Mathematical Sciences, ISSN 1072-3374, 2/2018, Volume 228, Issue 6, pp. 601 - 632

... FOR SOME NON-FREDHOLM INTEGRO-DIFFERENTIAL EQUA TIONS V. Vougalter ∗ University of Toronto 27 King’s College Circle Toronto, Ontario M5S 1A1, Canada vitali...

Mathematics, general | Mathematics | Differential equations | INTEGRALS | MATHEMATICAL SOLUTIONS | DIFFUSION EQUATIONS | MATHEMATICAL SPACE | CONVERGENCE | INTEGRO-DIFFERENTIAL EQUATIONS | MATHEMATICAL METHODS AND COMPUTING | DIFFERENTIAL OPERATORS | KERNELS

Mathematics, general | Mathematics | Differential equations | INTEGRALS | MATHEMATICAL SOLUTIONS | DIFFUSION EQUATIONS | MATHEMATICAL SPACE | CONVERGENCE | INTEGRO-DIFFERENTIAL EQUATIONS | MATHEMATICAL METHODS AND COMPUTING | DIFFERENTIAL OPERATORS | KERNELS

Journal Article

Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, 2012, Volume 7, Issue 2, pp. 146 - 154

We obtain solvability conditions in H-6(R-3) for a sixth order partial differential equation which is the linearized Cahn-Hilliard problem using the results...

Sobolev spaces | Solvability conditions | Non Fredholm operators | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | STATIONARY SOLUTIONS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | solvability conditions | non Fredholm operators | Partial differential equations | Mathematical models | Analysis of PDEs | Mathematics

Sobolev spaces | Solvability conditions | Non Fredholm operators | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | STATIONARY SOLUTIONS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | solvability conditions | non Fredholm operators | Partial differential equations | Mathematical models | Analysis of PDEs | Mathematics

Journal Article

Applied Mathematical Modelling, ISSN 0307-904X, 02/2017, Volume 42, pp. 591 - 599

•A new type of reaction–diffusion equations with two nonlocal terms is studied.•Nonlocal consumption and reproduction with different phenotypes are...

Emergence of species | Traveling waves | Reaction–diffusion equation | Stationary pulses | Nonlocal reproduction | STATES | POPULATIONS | PATTERNS | MODEL | TRAVELING-WAVES | Reaction-diffusion equation | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EVOLUTION | ENGINEERING, MULTIDISCIPLINARY | DYNAMICS | FISHER-KPP EQUATION | Analysis | Numerical analysis | Population biology | Analysis of PDEs | Mathematics

Emergence of species | Traveling waves | Reaction–diffusion equation | Stationary pulses | Nonlocal reproduction | STATES | POPULATIONS | PATTERNS | MODEL | TRAVELING-WAVES | Reaction-diffusion equation | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EVOLUTION | ENGINEERING, MULTIDISCIPLINARY | DYNAMICS | FISHER-KPP EQUATION | Analysis | Numerical analysis | Population biology | Analysis of PDEs | Mathematics

Journal Article

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, ISSN 0035-7596, 2017, Volume 47, Issue 3, pp. 955 - 970

In this article, we establish the existence of solutions of a system of integro-differential equations arising in population dynamics in the case of anomalous...

MATHEMATICS | ANOMALOUS DIFFUSION | HOLDER THEORY | PROPERTY | SOLVABILITY CONDITIONS | DIRICHLET | OPERATORS | Analysis of PDEs | Mathematics

MATHEMATICS | ANOMALOUS DIFFUSION | HOLDER THEORY | PROPERTY | SOLVABILITY CONDITIONS | DIRICHLET | OPERATORS | Analysis of PDEs | Mathematics

Journal Article

Journal of Dynamics and Differential Equations, ISSN 1040-7294, 9/2017, Volume 29, Issue 3, pp. 1145 - 1158

Reaction-diffusion equations with a space dependent nonlinearity are considered on the whole axis. Existence of pulses, stationary solutions which vanish at...

Reaction-diffusion equation | Ordinary Differential Equations | 35A16 | 92D15 | Leray–Schauder method | Mathematics | Applications of Mathematics | 35K57 | Existence of pulse solutions | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Leray-Schauder method | POSITIVE SOLUTIONS | BEHAVIOR | NONLINEAR ELLIPTIC-EQUATIONS | Analysis of PDEs

Reaction-diffusion equation | Ordinary Differential Equations | 35A16 | 92D15 | Leray–Schauder method | Mathematics | Applications of Mathematics | 35K57 | Existence of pulse solutions | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Leray-Schauder method | POSITIVE SOLUTIONS | BEHAVIOR | NONLINEAR ELLIPTIC-EQUATIONS | Analysis of PDEs

Journal Article

Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, 3/2018, Volume 9, Issue 1, pp. 25 - 46

... operators similarly to our preceding work (V olpert and V ougalter in Electron J Differ Equ 160:16, 2013). Keywords Solvability conditions · Non Fredholm operators...

35J10 | Non Fredholm operators | Mathematics | 35P10 | Solvability conditions | Operator Theory | Algebra | Functional Analysis | Analysis | Applications of Mathematics | Sobolev spaces | Partial Differential Equations | 47F05 | MATHEMATICS | MATHEMATICS, APPLIED | HOLDER THEORY | DIFFUSION | POTENTIALS | EQUATION | Sequences (Mathematics) | Research | Mathematical research | Mappings (Mathematics) | Analysis of PDEs

35J10 | Non Fredholm operators | Mathematics | 35P10 | Solvability conditions | Operator Theory | Algebra | Functional Analysis | Analysis | Applications of Mathematics | Sobolev spaces | Partial Differential Equations | 47F05 | MATHEMATICS | MATHEMATICS, APPLIED | HOLDER THEORY | DIFFUSION | POTENTIALS | EQUATION | Sequences (Mathematics) | Research | Mathematical research | Mappings (Mathematics) | Analysis of PDEs

Journal Article

Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, 01/2010, Volume 5, Issue 4, pp. 448 - 469

We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues...

NLS equation | Birman-Schwinger principle | spectral stability | Feshbach map | EXISTENCE | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | BIFURCATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITARY WAVES | MATHEMATICAL & COMPUTATIONAL BIOLOGY | ASYMPTOTIC STABILITY | SPECTRA | GROUND-STATES

NLS equation | Birman-Schwinger principle | spectral stability | Feshbach map | EXISTENCE | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | BIFURCATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITARY WAVES | MATHEMATICAL & COMPUTATIONAL BIOLOGY | ASYMPTOTIC STABILITY | SPECTRA | GROUND-STATES

Journal Article

Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, 3/2018, Volume 9, Issue 1, pp. 1 - 24

We prove the existence of stationary solutions for some reaction-diffusion equations with superdiffusion. The corresponding elliptic problem contains the...

35J10 | Non Fredholm operators | Integro-differential equations | Mathematics | Solvability conditions | 35P30 | 35K57 | Operator Theory | Superdiffusion | Algebra | Functional Analysis | Analysis | Applications of Mathematics | Stationary solutions | Partial Differential Equations | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, APPLIED | DYNAMICS | MODEL | TRAVELING-WAVES | Fixed point theory | Usage | Research | Heat equation | Mathematical research | Mappings (Mathematics) | Analysis of PDEs

35J10 | Non Fredholm operators | Integro-differential equations | Mathematics | Solvability conditions | 35P30 | 35K57 | Operator Theory | Superdiffusion | Algebra | Functional Analysis | Analysis | Applications of Mathematics | Stationary solutions | Partial Differential Equations | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, APPLIED | DYNAMICS | MODEL | TRAVELING-WAVES | Fixed point theory | Usage | Research | Heat equation | Mathematical research | Mappings (Mathematics) | Analysis of PDEs

Journal Article

Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova, ISSN 0041-8994, 2017, Volume 137, pp. 185 - 201

The work deals with the existence of solutions of an integro-differential equation arising in population dynamics in the case of anomalous diffusion. The proof...

Sobolev spaces | Integro-differential equations | Non Fredholm operators | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, APPLIED | HOLDER THEORY | PROPERTY | SOLVABILITY CONDITIONS | non Fredholm operators | DIRICHLET | OPERATORS

Sobolev spaces | Integro-differential equations | Non Fredholm operators | MATHEMATICS | ANOMALOUS DIFFUSION | MATHEMATICS, APPLIED | HOLDER THEORY | PROPERTY | SOLVABILITY CONDITIONS | non Fredholm operators | DIRICHLET | OPERATORS

Journal Article

Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 02/2011, Volume 54, Issue 1, pp. 249 - 271

... for Schrödinger-type operators. One of the main results of the paper concerns solvability conditions for the equation –Δu + V(x)u–au = f where a ≥ 0...

elliptic problems | non-Fredholm operators | solvability conditions | MATHEMATICS | HOLDER THEORY | NULL-SPACES | SYSTEMS | PARTIAL DIFFERENTIAL OPERATORS | ELLIPTIC-OPERATORS | Mathematical problems | Partial differential equations | Mathematical analysis | Operators | Spectral theory | Orthogonality | Scattering | Adjoints | Analysis of PDEs | Mathematics

elliptic problems | non-Fredholm operators | solvability conditions | MATHEMATICS | HOLDER THEORY | NULL-SPACES | SYSTEMS | PARTIAL DIFFERENTIAL OPERATORS | ELLIPTIC-OPERATORS | Mathematical problems | Partial differential equations | Mathematical analysis | Operators | Spectral theory | Orthogonality | Scattering | Adjoints | Analysis of PDEs | Mathematics

Journal Article

Communications on Pure and Applied Analysis, ISSN 1534-0392, 01/2012, Volume 11, Issue 1, pp. 365 - 373

A linear second order elliptic equation describing heat or mass diffusion and convection on a given velocity field is considered in R-3. The corresponding...

Adjoint operator | Solvability conditions | Continuous spectrum | Porous medium | MATHEMATICS | MATHEMATICS, APPLIED | adjoint operator | porous medium | continuous spectrum

Adjoint operator | Solvability conditions | Continuous spectrum | Porous medium | MATHEMATICS | MATHEMATICS, APPLIED | adjoint operator | porous medium | continuous spectrum

Journal Article

Journal of mathematical sciences (New York, N.Y.), ISSN 1072-3374, 06/2020, Volume 247, Issue 6, pp. 850 - 864

Journal Article

Analysis and Mathematical Physics, ISSN 1664-2368, 12/2012, Volume 2, Issue 4, pp. 473 - 496

We obtain solvability conditions in $$H^{2}$$ for some elliptic equations in cylindrical domains using the methods of spectral theory and scattering theory for...

35J10 | Mathematical Methods in Physics | Non Fredholm operators | 35J60 | Analysis | 35P25 | Elliptic problems | Mathematics | 35P10 | Solvability conditions | Embedded solitons | MATHEMATICS | MATHEMATICS, APPLIED | Analysis of PDEs

35J10 | Mathematical Methods in Physics | Non Fredholm operators | 35J60 | Analysis | 35P25 | Elliptic problems | Mathematics | 35P10 | Solvability conditions | Embedded solitons | MATHEMATICS | MATHEMATICS, APPLIED | Analysis of PDEs

Journal Article

Documenta Mathematica, ISSN 1431-0635, 2014, Volume 19, Issue 2014, pp. 1141 - 1154

A nonlocal reaction-diffusion equation and a system of equations from population dynamics are considered on the whole axis. Existence of solutions in the form...

Perturbation methods | Existence of pulse solutions | Reaction-diffusion equation | reaction-diffusion equation | MATHEMATICS | STABILITY | DYNAMICS | PATTERNS | existence of pulse solutions | perturbation methods | SPATIAL STRUCTURES | TRAVELING-WAVES | Analysis of PDEs | Mathematics

Perturbation methods | Existence of pulse solutions | Reaction-diffusion equation | reaction-diffusion equation | MATHEMATICS | STABILITY | DYNAMICS | PATTERNS | existence of pulse solutions | perturbation methods | SPATIAL STRUCTURES | TRAVELING-WAVES | Analysis of PDEs | Mathematics

Journal Article

Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, 2015, Volume 40, Issue 1, pp. 321 - 328

We establish the existence in H-3(R-5) of stationary solutions of certain nonlinear heat equations using the Fixed Point Technique. The equation for the...

Sobolev spaces | Non fredholm operators | Nonlinear heat equations | MATHEMATICS | HOLDER THEORY | PROPERTY | SOLVABILITY CONDITIONS | non Fredholm operators | DIRICHLET | OPERATORS

Sobolev spaces | Non fredholm operators | Nonlinear heat equations | MATHEMATICS | HOLDER THEORY | PROPERTY | SOLVABILITY CONDITIONS | non Fredholm operators | DIRICHLET | OPERATORS

Journal Article

Electronic Journal of Differential Equations, ISSN 1072-6691, 10/2015, Volume 2015, Issue 264, pp. 1 - 10

In this article we study the interaction of two miscible liquids in porous media. The model consists of hydrodynamic equations with the Korteweg stress terms...

Porous media | Darcy approximation | Korteweg stress | Miscible liquids | FLUIDS | MATHEMATICS | MATHEMATICS, APPLIED | DIFFUSE INTERFACES | SYSTEMS | miscible liquids | porous media | STRESSES | Analysis of PDEs | Mathematics

Porous media | Darcy approximation | Korteweg stress | Miscible liquids | FLUIDS | MATHEMATICS | MATHEMATICS, APPLIED | DIFFUSE INTERFACES | SYSTEMS | miscible liquids | porous media | STRESSES | Analysis of PDEs | Mathematics

Journal Article

Electronic Journal of Differential Equations, ISSN 1072-6691, 2013, Volume 2013, Issue 160, pp. 1 - 16

We study the solvability of certain linear nonhomogeneous elliptic problems and show that under reasonable technical conditions the convergence in L-2(R-d) of...

Sobolev spaces | Solvability conditions | Non Fredholm operators | MATHEMATICS | MATHEMATICS, APPLIED | non Fredholm operators | POTENTIALS | EQUATION | Analysis of PDEs | Mathematics

Sobolev spaces | Solvability conditions | Non Fredholm operators | MATHEMATICS | MATHEMATICS, APPLIED | non Fredholm operators | POTENTIALS | EQUATION | Analysis of PDEs | Mathematics

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 11/2015, Volume 27, Issue 10, p. 1550023

We show global well-posedness in energy norm of the semi-relativistic Schrödinger–Poisson system of equations with attractive Coulomb interaction in ℝ 3 in the...

blow up of solutions | global existence | pseudo-relativistic diffusion | Schrödinger-Poisson system | fractional Laplacian | functional spaces | mean-field dynamics | density matrices | Cauchy problem | Schrodinger-Poisson system | EQUATIONS | WELL-POSEDNESS | PHYSICS, MATHEMATICAL | NLS

blow up of solutions | global existence | pseudo-relativistic diffusion | Schrödinger-Poisson system | fractional Laplacian | functional spaces | mean-field dynamics | density matrices | Cauchy problem | Schrodinger-Poisson system | EQUATIONS | WELL-POSEDNESS | PHYSICS, MATHEMATICAL | NLS

Journal Article

Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 05/2010, Volume 13, Issue 3, pp. 537 - 557

Some models in population dynamics with intra-specific competition lead to integro-differential equations where the integral term corresponds to nonlocal...

Integro-differential equations | Population dynamics | Generalized travelling waves | DYNAMICS | MATHEMATICS, APPLIED | generalized travelling waves | population dynamics | FRONT PROPAGATION

Integro-differential equations | Population dynamics | Generalized travelling waves | DYNAMICS | MATHEMATICS, APPLIED | generalized travelling waves | population dynamics | FRONT PROPAGATION

Journal Article

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