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Boundary layer and variational eigencurve in two-parameter single pendulum type equations
Nonuniqueness of solutions to semilinear parabolic equations with singular coefficients
| 1. | Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza” P.le A. Moro 5, I-00185, Roma, Italy |
| 2. | Depto. de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avda. de la Universidad 30, Leganés 28911, Madrid, Spain |
| 3. | Dipartimento di Matematica "G. Castelnuovo", Università di Roma "La Sapienza", P.le A. Moro 5, I-00185 Roma |
| [1] |
Gisèle Ruiz Goldstein, Jerome A. Goldstein, Abdelaziz Rhandi. Kolmogorov equations perturbed by an inverse-square potential. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 623-630. doi: 10.3934/dcdss.2011.4.623 |
| [2] |
Toshiyuki Suzuki. Scattering theory for semilinear Schrödinger equations with an inverse-square potential via energy methods. Evolution Equations and Control Theory, 2019, 8 (2) : 447-471. doi: 10.3934/eect.2019022 |
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Maria Assunta Pozio, Fabio Punzo, Alberto Tesei. Uniqueness and nonuniqueness of solutions to parabolic problems with singular coefficients. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 891-916. doi: 10.3934/dcds.2011.30.891 |
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Doyoon Kim, Kyeong-Hun Kim, Kijung Lee. Parabolic Systems with measurable coefficients in weighted Sobolev spaces. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022062 |
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Veronica Felli, Ana Primo. Classification of local asymptotics for solutions to heat equations with inverse-square potentials. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 65-107. doi: 10.3934/dcds.2011.31.65 |
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Umberto Biccari. Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential. Mathematical Control and Related Fields, 2019, 9 (1) : 191-219. doi: 10.3934/mcrf.2019011 |
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Doyoon Kim, Hongjie Dong, Hong Zhang. Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4895-4914. doi: 10.3934/dcds.2016011 |
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Toshiyuki Suzuki. Semilinear Schrödinger evolution equations with inverse-square and harmonic potentials via pseudo-conformal symmetry. Communications on Pure and Applied Analysis, 2021, 20 (12) : 4347-4377. doi: 10.3934/cpaa.2021163 |
| [9] |
Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh. $L^p$ Estimates for the wave equation with the inverse-square potential. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 427-442. doi: 10.3934/dcds.2003.9.427 |
| [10] |
Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh. Dispersive estimate for the wave equation with the inverse-square potential. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 1387-1400. doi: 10.3934/dcds.2003.9.1387 |
| [11] |
Rowan Killip, Changxing Miao, Monica Visan, Junyong Zhang, Jiqiang Zheng. The energy-critical NLS with inverse-square potential. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3831-3866. doi: 10.3934/dcds.2017162 |
| [12] |
Yaoping Chen, Jianqing Chen. Existence of multiple positive weak solutions and estimates for extremal values for a class of concave-convex elliptic problems with an inverse-square potential. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1531-1552. doi: 10.3934/cpaa.2017073 |
| [13] |
Toshiyuki Suzuki. Energy methods for Hartree type equations with inverse-square potentials. Evolution Equations and Control Theory, 2013, 2 (3) : 531-542. doi: 10.3934/eect.2013.2.531 |
| [14] |
Hyeongjin Lee, Ihyeok Seo, Jihyeon Seok. Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 597-608. doi: 10.3934/dcds.2020024 |
| [15] |
Rui Zhang, Yong-Kui Chang, G. M. N'Guérékata. Weighted pseudo almost automorphic mild solutions to semilinear integral equations with $S^{p}$-weighted pseudo almost automorphic coefficients. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5525-5537. doi: 10.3934/dcds.2013.33.5525 |
| [16] |
Patrick Martinez, Judith Vancostenoble. The cost of boundary controllability for a parabolic equation with inverse square potential. Evolution Equations and Control Theory, 2019, 8 (2) : 397-422. doi: 10.3934/eect.2019020 |
| [17] |
Toshiyuki Suzuki. Nonlinear Schrödinger equations with inverse-square potentials in two dimensional space. Conference Publications, 2015, 2015 (special) : 1019-1024. doi: 10.3934/proc.2015.1019 |
| [18] |
Lei Wei, Xiyou Cheng, Zhaosheng Feng. Exact behavior of positive solutions to elliptic equations with multi-singular inverse square potentials. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 7169-7189. doi: 10.3934/dcds.2016112 |
| [19] |
Jian Zhang, Wen Zhang, Xianhua Tang. Ground state solutions for Hamiltonian elliptic system with inverse square potential. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4565-4583. doi: 10.3934/dcds.2017195 |
| [20] |
Kazuhiro Ishige, Asato Mukai. Large time behavior of solutions of the heat equation with inverse square potential. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 4041-4069. doi: 10.3934/dcds.2018176 |
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