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Preface on the special issue of Discrete and Continuous Dynamical Systems- Series B in honor of Chris Cosner on the occasion of his 60th birthday
Some paradoxical effects of the advection on a class of diffusive equations in Ecology
1. | Department of Mathematics, University Carlos III of Madrid, Leganés (Madrid), 28911, Spain |
2. | Department of Applied Mathematics, Complutense University of Madrid, Madrid, 28040, Spain |
References:
[1] |
H. Amann, On the existence of positive solutions of nonlinear elliptic boundary value problems,, Indiana J. Mathematics, 21 (1972), 125.
doi: 10.1512/iumj.1972.21.21012. |
[2] |
H. Amann and J. López-Gómez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems,, J. Diff. Equations, 146 (1998), 336.
doi: 10.1006/jdeq.1998.3440. |
[3] |
F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environments,, Can. Appl. Math. Quart., 3 (1995), 379.
|
[4] |
H. Berestycki, F. Hamel and N. Nadirashvili, Elliptic eigenvalue problems with latge drift and applications to nonlinear propagation phenomena,, Commun. Math. Phys., 253 (2005), 451.
doi: 10.1007/s00220-004-1201-9. |
[5] |
K. J. Brown and S. S. Lin, On the existence of principal eigenfunctions for an eigenvalue problem with indefinite weight function,, J. Math. Anal. Appns., 75 (1980), 112.
doi: 10.1016/0022-247X(80)90309-1. |
[6] |
S. Cano-Casanova and J. López-Gómez, Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems,, J. Diff. Equations, 178 (2002), 123.
doi: 10.1006/jdeq.2000.4003. |
[7] |
X. Chen and Y. Lou, Principal eigenvaue and eigenfunctions of an elliptic operator with large advection and its application to a competition model,, Indiana Univ. Math. J., 57 (2008), 627.
doi: 10.1512/iumj.2008.57.3204. |
[8] |
M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues,, J. Funct. Anal., 8 (1971), 321.
doi: 10.1016/0022-1236(71)90015-2. |
[9] |
E. N. Dancer and J. López-Gómez, Semiclassical analysis of general second order elliptic operators on bounded domains,, Trans. Amer. Math. Soc., 352 (2000), 3723.
doi: 10.1090/S0002-9947-00-02534-4. |
[10] |
J. E. Furter and J. López-Gómez, Diffusion mediated permanence problem for a heterogeneous Lotka-Volterra competition model,, Proc. Royal Soc. Edinburgh, 127 (1997), 281.
doi: 10.1017/S0308210500023659. |
[11] |
R. Gómez-Reñasco, The Effects of Varying Coefficents in Semilinear Elliptic Boundary Value Problems. From Classical Solutons to Metasolutions,, Ph.D Thesis, (1999). Google Scholar |
[12] |
R. Gómez-Reñasco and J. López-Gómez, On the existence and numerical computation of classical and non-classical solutions for a family of elliptic boundary value problems,, Nonl. Anal. T.M.A., 48 (2002), 567.
doi: 10.1016/S0362-546X(00)00208-X. |
[13] |
P. Hess and T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function,, Comm. Part. Diff. Eqns., 5 (1980), 999.
doi: 10.1080/03605308008820162. |
[14] |
V. Hutson, J. López-Gómez, K. Mischaikow and G. Vickers, Limit behaviour for a competing species problem with diffusion,, in World Scientific Series in Applied Analysis, 4 (1995), 343.
doi: 10.1142/9789812796417_0022. |
[15] |
T. Kato, Perturbation Theory for Linear Operators,, Classics in Mathematics, (1995).
|
[16] |
J. López-Gómez, On linear weighted boundary value problems,, in Partial Differential Equations, 82 (1994), 188.
|
[17] |
J. López-Gómez, The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems,, J. Diff. Equations, 127 (1996), 263.
doi: 10.1006/jdeq.1996.0070. |
[18] |
J. López-Gómez, Large solutions, metasolutions, and asymptotic behaviour of the regular positive solutions of sublinear parabolic problems,, El. J. Diff. Equations, 5 (2000), 135.
|
[19] |
J. López-Gómez, Approaching metasolutions by solutions,, Diff. Int. Eqns., 14 (2001), 739.
|
[20] |
J. López-Gómez, Metasolutions: Malthus versus Verhulst in population dynamics. A dream of Volterra,, in Handbook of Differential Equations, 2 (2005), 211.
doi: 10.1016/S1874-5733(05)80012-9. |
[21] |
J. López-Gómez, Spectral Theory and Nonlinear Functional Analysis,, Research Notes in Mathematics 426, (2001).
doi: 10.1201/9781420035506. |
[22] |
J. López-Gómez, Elliptic Operators,, World Scientific Publishing, (2013). Google Scholar |
[23] |
J. López-Gómez and M. Molina-Meyer, The maximum principle for cooperative weakly coupled elliptic systems and some applications,, Diff. Int. Eqns., 7 (1994), 383.
|
[24] |
J. López-Gómez and M. Montenegro, The effects of transport on the maximum principle,, J. Math. Anal. Appl., 403 (2013), 547.
doi: 10.1016/j.jmaa.2013.02.049. |
[25] |
A. Manes and A. M. Micheletti, Un'estensione della teoria variazionale classica degli autovalori per operatori ellitici del secondo ordine,, Boll. Un. Mat. Italiana, 7 (1973), 285.
|
[26] |
D. Sattinger, Topics in Stability and Bifurcation Theory,, Lecture Notes in Mathematics 309, (1973).
|
[27] |
S. Senn, On a semilinear elliptic eigenvalue problem with Neumann boundary conditions, with an application to population genetics,, Comm. Part. Diff. Eqns., 8 (1983), 1199.
doi: 10.1080/03605308308820300. |
[28] |
S. Senn and P. Hess, On positive solutions of a linear elliptic boundary value problem with Neumann boundary conditions,, Math. Annalen, 258 (1982), 459.
doi: 10.1007/BF01453979. |
[29] |
E. M. Stein, Singular Integrals and Differentiability Properties of Functions,, Princeton University Press, (1970).
|
show all references
References:
[1] |
H. Amann, On the existence of positive solutions of nonlinear elliptic boundary value problems,, Indiana J. Mathematics, 21 (1972), 125.
doi: 10.1512/iumj.1972.21.21012. |
[2] |
H. Amann and J. López-Gómez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems,, J. Diff. Equations, 146 (1998), 336.
doi: 10.1006/jdeq.1998.3440. |
[3] |
F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environments,, Can. Appl. Math. Quart., 3 (1995), 379.
|
[4] |
H. Berestycki, F. Hamel and N. Nadirashvili, Elliptic eigenvalue problems with latge drift and applications to nonlinear propagation phenomena,, Commun. Math. Phys., 253 (2005), 451.
doi: 10.1007/s00220-004-1201-9. |
[5] |
K. J. Brown and S. S. Lin, On the existence of principal eigenfunctions for an eigenvalue problem with indefinite weight function,, J. Math. Anal. Appns., 75 (1980), 112.
doi: 10.1016/0022-247X(80)90309-1. |
[6] |
S. Cano-Casanova and J. López-Gómez, Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems,, J. Diff. Equations, 178 (2002), 123.
doi: 10.1006/jdeq.2000.4003. |
[7] |
X. Chen and Y. Lou, Principal eigenvaue and eigenfunctions of an elliptic operator with large advection and its application to a competition model,, Indiana Univ. Math. J., 57 (2008), 627.
doi: 10.1512/iumj.2008.57.3204. |
[8] |
M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues,, J. Funct. Anal., 8 (1971), 321.
doi: 10.1016/0022-1236(71)90015-2. |
[9] |
E. N. Dancer and J. López-Gómez, Semiclassical analysis of general second order elliptic operators on bounded domains,, Trans. Amer. Math. Soc., 352 (2000), 3723.
doi: 10.1090/S0002-9947-00-02534-4. |
[10] |
J. E. Furter and J. López-Gómez, Diffusion mediated permanence problem for a heterogeneous Lotka-Volterra competition model,, Proc. Royal Soc. Edinburgh, 127 (1997), 281.
doi: 10.1017/S0308210500023659. |
[11] |
R. Gómez-Reñasco, The Effects of Varying Coefficents in Semilinear Elliptic Boundary Value Problems. From Classical Solutons to Metasolutions,, Ph.D Thesis, (1999). Google Scholar |
[12] |
R. Gómez-Reñasco and J. López-Gómez, On the existence and numerical computation of classical and non-classical solutions for a family of elliptic boundary value problems,, Nonl. Anal. T.M.A., 48 (2002), 567.
doi: 10.1016/S0362-546X(00)00208-X. |
[13] |
P. Hess and T. Kato, On some linear and nonlinear eigenvalue problems with an indefinite weight function,, Comm. Part. Diff. Eqns., 5 (1980), 999.
doi: 10.1080/03605308008820162. |
[14] |
V. Hutson, J. López-Gómez, K. Mischaikow and G. Vickers, Limit behaviour for a competing species problem with diffusion,, in World Scientific Series in Applied Analysis, 4 (1995), 343.
doi: 10.1142/9789812796417_0022. |
[15] |
T. Kato, Perturbation Theory for Linear Operators,, Classics in Mathematics, (1995).
|
[16] |
J. López-Gómez, On linear weighted boundary value problems,, in Partial Differential Equations, 82 (1994), 188.
|
[17] |
J. López-Gómez, The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems,, J. Diff. Equations, 127 (1996), 263.
doi: 10.1006/jdeq.1996.0070. |
[18] |
J. López-Gómez, Large solutions, metasolutions, and asymptotic behaviour of the regular positive solutions of sublinear parabolic problems,, El. J. Diff. Equations, 5 (2000), 135.
|
[19] |
J. López-Gómez, Approaching metasolutions by solutions,, Diff. Int. Eqns., 14 (2001), 739.
|
[20] |
J. López-Gómez, Metasolutions: Malthus versus Verhulst in population dynamics. A dream of Volterra,, in Handbook of Differential Equations, 2 (2005), 211.
doi: 10.1016/S1874-5733(05)80012-9. |
[21] |
J. López-Gómez, Spectral Theory and Nonlinear Functional Analysis,, Research Notes in Mathematics 426, (2001).
doi: 10.1201/9781420035506. |
[22] |
J. López-Gómez, Elliptic Operators,, World Scientific Publishing, (2013). Google Scholar |
[23] |
J. López-Gómez and M. Molina-Meyer, The maximum principle for cooperative weakly coupled elliptic systems and some applications,, Diff. Int. Eqns., 7 (1994), 383.
|
[24] |
J. López-Gómez and M. Montenegro, The effects of transport on the maximum principle,, J. Math. Anal. Appl., 403 (2013), 547.
doi: 10.1016/j.jmaa.2013.02.049. |
[25] |
A. Manes and A. M. Micheletti, Un'estensione della teoria variazionale classica degli autovalori per operatori ellitici del secondo ordine,, Boll. Un. Mat. Italiana, 7 (1973), 285.
|
[26] |
D. Sattinger, Topics in Stability and Bifurcation Theory,, Lecture Notes in Mathematics 309, (1973).
|
[27] |
S. Senn, On a semilinear elliptic eigenvalue problem with Neumann boundary conditions, with an application to population genetics,, Comm. Part. Diff. Eqns., 8 (1983), 1199.
doi: 10.1080/03605308308820300. |
[28] |
S. Senn and P. Hess, On positive solutions of a linear elliptic boundary value problem with Neumann boundary conditions,, Math. Annalen, 258 (1982), 459.
doi: 10.1007/BF01453979. |
[29] |
E. M. Stein, Singular Integrals and Differentiability Properties of Functions,, Princeton University Press, (1970).
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