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Existence of a stable set for some nonlinear parabolic equation involving critical Sobolev exponent
1. | Department of Mathematical Sciences,, School of Science and Engineering, Waseda University, 169-855, 4-1 Okubo 3-chome, Shinjyuku-ku, Tokyo, Japan |
[1] |
M. A. Efendiev. On the compactness of the stable set for rate independent processes. Communications on Pure and Applied Analysis, 2003, 2 (4) : 495-509. doi: 10.3934/cpaa.2003.2.495 |
[2] |
Erisa Hasani, Kanishka Perera. On the compactness threshold in the critical Kirchhoff equation. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 1-19. doi: 10.3934/dcds.2021106 |
[3] |
D. Bartolucci, L. Orsina. Uniformly elliptic Liouville type equations: concentration compactness and a priori estimates. Communications on Pure and Applied Analysis, 2005, 4 (3) : 499-522. doi: 10.3934/cpaa.2005.4.499 |
[4] |
Alain Bensoussan, Miroslav Bulíček, Jens Frehse. Existence and compactness for weak solutions to Bellman systems with critical growth. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1729-1750. doi: 10.3934/dcdsb.2012.17.1729 |
[5] |
Carlo Mercuri, Michel Willem. A global compactness result for the p-Laplacian involving critical nonlinearities. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 469-493. doi: 10.3934/dcds.2010.28.469 |
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Yanfang Peng. On elliptic systems with Sobolev critical exponent. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3357-3373. doi: 10.3934/dcds.2016.36.3357 |
[7] |
Roberto Livrea, Salvatore A. Marano. A min-max principle for non-differentiable functions with a weak compactness condition. Communications on Pure and Applied Analysis, 2009, 8 (3) : 1019-1029. doi: 10.3934/cpaa.2009.8.1019 |
[8] |
Pavel Jirásek. On Compactness Conditions for the $p$-Laplacian. Communications on Pure and Applied Analysis, 2016, 15 (3) : 715-726. doi: 10.3934/cpaa.2016.15.715 |
[9] |
Wenmin Gong, Guangcun Lu. On Dirac equation with a potential and critical Sobolev exponent. Communications on Pure and Applied Analysis, 2015, 14 (6) : 2231-2263. doi: 10.3934/cpaa.2015.14.2231 |
[10] |
Lorenzo Brasco, Marco Squassina, Yang Yang. Global compactness results for nonlocal problems. Discrete and Continuous Dynamical Systems - S, 2018, 11 (3) : 391-424. doi: 10.3934/dcdss.2018022 |
[11] |
Daniel Faraco, Jan Kristensen. Compactness versus regularity in the calculus of variations. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 473-485. doi: 10.3934/dcdsb.2012.17.473 |
[12] |
Li Ma. Blow-up for semilinear parabolic equations with critical Sobolev exponent. Communications on Pure and Applied Analysis, 2013, 12 (2) : 1103-1110. doi: 10.3934/cpaa.2013.12.1103 |
[13] |
T. Ogawa. The degenerate drift-diffusion system with the Sobolev critical exponent. Discrete and Continuous Dynamical Systems - S, 2011, 4 (4) : 875-886. doi: 10.3934/dcdss.2011.4.875 |
[14] |
Xiaomei Sun, Wenyi Chen. Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent. Communications on Pure and Applied Analysis, 2011, 10 (2) : 527-540. doi: 10.3934/cpaa.2011.10.527 |
[15] |
Peng Chen, Xiaochun Liu. Multiplicity of solutions to Kirchhoff type equations with critical Sobolev exponent. Communications on Pure and Applied Analysis, 2018, 17 (1) : 113-125. doi: 10.3934/cpaa.2018007 |
[16] |
Kaimin Teng, Xiumei He. Ground state solutions for fractional Schrödinger equations with critical Sobolev exponent. Communications on Pure and Applied Analysis, 2016, 15 (3) : 991-1008. doi: 10.3934/cpaa.2016.15.991 |
[17] |
Guangze Gu, Xianhua Tang, Youpei Zhang. Ground states for asymptotically periodic fractional Kirchhoff equation with critical Sobolev exponent. Communications on Pure and Applied Analysis, 2019, 18 (6) : 3181-3200. doi: 10.3934/cpaa.2019143 |
[18] |
Yong Zhou, V. Vijayakumar, R. Murugesu. Controllability for fractional evolution inclusions without compactness. Evolution Equations and Control Theory, 2015, 4 (4) : 507-524. doi: 10.3934/eect.2015.4.507 |
[19] |
Jing Zhang, Shiwang Ma. Positive solutions of perturbed elliptic problems involving Hardy potential and critical Sobolev exponent. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1999-2009. doi: 10.3934/dcdsb.2016033 |
[20] |
M. L. Miotto. Multiple solutions for elliptic problem in $\mathbb{R}^N$ with critical Sobolev exponent and weight function. Communications on Pure and Applied Analysis, 2010, 9 (1) : 233-248. doi: 10.3934/cpaa.2010.9.233 |
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