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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
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
Journal Article
Mathematical Modelling of Natural Phenomena, ISSN 0973-5348, 2012, Volume 7, Issue 2, pp. 146 - 154
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 02/2017, Volume 42, pp. 591 - 599
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
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
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
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
Journal Article
Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, 3/2018, Volume 9, Issue 1, pp. 1 - 24
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
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
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
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
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
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
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
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
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
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
Journal Article
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