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On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density
Ground states for scalar field equations with anisotropic nonlocal nonlinearities
1. | Department of Mathematics and Computer Science, University of Cagliari, Viale L. Merello 92, 09123 Cagliari, Italy |
2. | Department of Mathematical Sciences, Florida Institute of Technology, 150 W University Blvd, Melbourne, FL 32901 |
3. | Dipartimento di Informatica, Università di Verona, Strada Le Grazie 15, 37134 Verona |
References:
[1] |
A. Bahri and P.-L. Lions, On the existence of a positive solution of semilinear elliptic equations in unbounded domains,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 14 (1997), 365.
doi: 10.1016/S0294-1449(97)80142-4. |
[2] |
V. Benci and G. Cerami, Positive solutions of some nonlinear elliptic problems in exterior domains,, Arch. Rational Mech. Anal., 99 (1987), 283.
doi: 10.1007/BF00282048. |
[3] |
H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. I. Existence of a ground state,, Arch. Rational Mech. Anal., 82 (1983), 313.
doi: 10.1007/BF00250555. |
[4] |
J. Byeon, L. Jeanjean and M. Mariş, Symmetry and monotonicity of least energy solutions,, Calc. Var. Partial Differential Equations, 36 (2009), 481.
doi: 10.1007/s00526-009-0238-1. |
[5] |
L. Diening, P. Harjulehto, P. Hästö and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents,, Lecture Notes in Mathematics, (2017).
doi: 10.1007/978-3-642-18363-8. |
[6] |
X. Fan and D. Zhao, On the spaces $L^{p(\cdot)}(\Omega)$ and $W^{m,p(x)}(\Omega)$,, J. Math. Anal. Appl., 263 (2001), 424.
doi: 10.1006/jmaa.2000.7617. |
[7] |
G. Franzina and P. Lindqvist, An eigenvalue problem with variable exponents,, Nonlinear Anal., 85 (2013), 1.
doi: 10.1016/j.na.2013.02.011. |
[8] |
M. K. Kwong, Uniqueness of positive solutions of $\Delta u-u+u^p=0$ in $\mathbbR^n$,, Arch. Rational Mech. Anal., 105 (1989), 243.
doi: 10.1007/BF00251502. |
[9] |
P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case I,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 109.
|
[10] |
P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case II,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 223.
|
[11] |
P.-L. Lions, Solutions of Hartree-Fock equations for Coulomb systems,, Comm. Math. Phys., 109 (1987), 33.
doi: 10.1007/BF01205672. |
[12] |
M. Mariş, On the symmetry of minimizers,, Arch. Rational Mech. Anal., 192 (2009), 311.
doi: 10.1007/s00205-008-0136-2. |
[13] |
S. Solimini, A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 12 (1995), 319.
|
[14] |
M. Struwe, Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems,, Ergebnisse der Mathematik und ihrer Grenzgebiete, (2008).
|
[15] |
K. Tintarev and K.-H. Fieseler, Concentration Compactness. Functional-Analytic Grounds and Applications,, Imperial College Press, (2007).
|
show all references
References:
[1] |
A. Bahri and P.-L. Lions, On the existence of a positive solution of semilinear elliptic equations in unbounded domains,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 14 (1997), 365.
doi: 10.1016/S0294-1449(97)80142-4. |
[2] |
V. Benci and G. Cerami, Positive solutions of some nonlinear elliptic problems in exterior domains,, Arch. Rational Mech. Anal., 99 (1987), 283.
doi: 10.1007/BF00282048. |
[3] |
H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. I. Existence of a ground state,, Arch. Rational Mech. Anal., 82 (1983), 313.
doi: 10.1007/BF00250555. |
[4] |
J. Byeon, L. Jeanjean and M. Mariş, Symmetry and monotonicity of least energy solutions,, Calc. Var. Partial Differential Equations, 36 (2009), 481.
doi: 10.1007/s00526-009-0238-1. |
[5] |
L. Diening, P. Harjulehto, P. Hästö and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents,, Lecture Notes in Mathematics, (2017).
doi: 10.1007/978-3-642-18363-8. |
[6] |
X. Fan and D. Zhao, On the spaces $L^{p(\cdot)}(\Omega)$ and $W^{m,p(x)}(\Omega)$,, J. Math. Anal. Appl., 263 (2001), 424.
doi: 10.1006/jmaa.2000.7617. |
[7] |
G. Franzina and P. Lindqvist, An eigenvalue problem with variable exponents,, Nonlinear Anal., 85 (2013), 1.
doi: 10.1016/j.na.2013.02.011. |
[8] |
M. K. Kwong, Uniqueness of positive solutions of $\Delta u-u+u^p=0$ in $\mathbbR^n$,, Arch. Rational Mech. Anal., 105 (1989), 243.
doi: 10.1007/BF00251502. |
[9] |
P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case I,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 109.
|
[10] |
P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case II,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1 (1984), 223.
|
[11] |
P.-L. Lions, Solutions of Hartree-Fock equations for Coulomb systems,, Comm. Math. Phys., 109 (1987), 33.
doi: 10.1007/BF01205672. |
[12] |
M. Mariş, On the symmetry of minimizers,, Arch. Rational Mech. Anal., 192 (2009), 311.
doi: 10.1007/s00205-008-0136-2. |
[13] |
S. Solimini, A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 12 (1995), 319.
|
[14] |
M. Struwe, Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems,, Ergebnisse der Mathematik und ihrer Grenzgebiete, (2008).
|
[15] |
K. Tintarev and K.-H. Fieseler, Concentration Compactness. Functional-Analytic Grounds and Applications,, Imperial College Press, (2007).
|
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