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On the existance of minimizers of the variable exponent Dirichlet energy integral
1. | Department of Mathematics and Statistics, P.O. Box 68, FI-00014 University of Helsinki, Finland |
[1] |
V. V. Motreanu. Uniqueness results for a Dirichlet problem with variable exponent. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1399-1410. doi: 10.3934/cpaa.2010.9.1399 |
[2] |
SYLWIA DUDEK, IWONA SKRZYPCZAK. Liouville theorems for elliptic problems in variable exponent spaces. Communications on Pure and Applied Analysis, 2017, 16 (2) : 513-532. doi: 10.3934/cpaa.2017026 |
[3] |
Yansheng Zhong, Yongqing Li. On a p-Laplacian eigenvalue problem with supercritical exponent. Communications on Pure and Applied Analysis, 2019, 18 (1) : 227-236. doi: 10.3934/cpaa.2019012 |
[4] |
V. V. Motreanu. Multiplicity of solutions for variable exponent Dirichlet problem with concave term. Discrete and Continuous Dynamical Systems - S, 2012, 5 (4) : 845-855. doi: 10.3934/dcdss.2012.5.845 |
[5] |
Anouar Bahrouni, VicenŢiu D. RĂdulescu. On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent. Discrete and Continuous Dynamical Systems - S, 2018, 11 (3) : 379-389. doi: 10.3934/dcdss.2018021 |
[6] |
Ángel Arroyo, Joonas Heino, Mikko Parviainen. Tug-of-war games with varying probabilities and the normalized p(x)-laplacian. Communications on Pure and Applied Analysis, 2017, 16 (3) : 915-944. doi: 10.3934/cpaa.2017044 |
[7] |
Carla Baroncini, Julián Fernández Bonder. An extension of a Theorem of V. Šverák to variable exponent spaces. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1987-2007. doi: 10.3934/cpaa.2015.14.1987 |
[8] |
Agnid Banerjee, Nicola Garofalo. On the Dirichlet boundary value problem for the normalized $p$-laplacian evolution. Communications on Pure and Applied Analysis, 2015, 14 (1) : 1-21. doi: 10.3934/cpaa.2015.14.1 |
[9] |
Li Yin, Jinghua Yao, Qihu Zhang, Chunshan Zhao. Multiple solutions with constant sign of a Dirichlet problem for a class of elliptic systems with variable exponent growth. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2207-2226. doi: 10.3934/dcds.2017095 |
[10] |
Antonio Greco, Giovanni Porru. Optimization problems for the energy integral of p-Laplace equations. Conference Publications, 2013, 2013 (special) : 301-310. doi: 10.3934/proc.2013.2013.301 |
[11] |
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 |
[12] |
Lujuan Yu. The asymptotic behaviour of the $ p(x) $-Laplacian Steklov eigenvalue problem. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2621-2637. doi: 10.3934/dcdsb.2020025 |
[13] |
Goro Akagi, Kei Matsuura. Well-posedness and large-time behaviors of solutions for a parabolic equation involving $p(x)$-Laplacian. Conference Publications, 2011, 2011 (Special) : 22-31. doi: 10.3934/proc.2011.2011.22 |
[14] |
Elhoussine Azroul, Abdelmoujib Benkirane, and Mohammed Shimi. On a nonlocal problem involving the fractional $ p(x,.) $-Laplacian satisfying Cerami condition. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3479-3495. doi: 10.3934/dcdss.2020425 |
[15] |
Said Taarabti. Positive solutions for the $ p(x)- $Laplacian : Application of the Nehari method. Discrete and Continuous Dynamical Systems - S, 2022, 15 (1) : 229-243. doi: 10.3934/dcdss.2021029 |
[16] |
Wei Dai, Zhao Liu, Guozhen Lu. Hardy-Sobolev type integral systems with Dirichlet boundary conditions in a half space. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1253-1264. doi: 10.3934/cpaa.2017061 |
[17] |
Mohammad A. Rammaha, Daniel Toundykov, Zahava Wilstein. Global existence and decay of energy for a nonlinear wave equation with $p$-Laplacian damping. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4361-4390. doi: 10.3934/dcds.2012.32.4361 |
[18] |
Salim A. Messaoudi, Ala A. Talahmeh. Blow up of negative initial-energy solutions of a system of nonlinear wave equations with variable-exponent nonlinearities. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 1233-1245. doi: 10.3934/dcdss.2021107 |
[19] |
P. Cerejeiras, U. Kähler, M. M. Rodrigues, N. Vieira. Hodge type decomposition in variable exponent spaces for the time-dependent operators: the Schrödinger case. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2253-2272. doi: 10.3934/cpaa.2014.13.2253 |
[20] |
Maria-Magdalena Boureanu. Fourth-order problems with Leray-Lions type operators in variable exponent spaces. Discrete and Continuous Dynamical Systems - S, 2019, 12 (2) : 231-243. doi: 10.3934/dcdss.2019016 |
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