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On nonsmooth global implicit function theorems for locally Lipschitz functions from Banach spaces to Euclidean spaces. (English) Zbl 1502.49014

MSC:

49J52 Nonsmooth analysis
46T20 Continuous and differentiable maps in nonlinear functional analysis
26B10 Implicit function theorems, Jacobians, transformations with several variables

References:

[1] Krantz, S. G.; Parks, H. R., The Implicit Function Theorem, History Theory and Applications (2013), Birkhauser · Zbl 1269.58003 · doi:10.1007/978-1-4614-5981-1
[2] Sunthrayuth, P.; Pakkaranang, N.; Kumam, P.; Thounthong, P.; Cholamjiak, P., Convergence theorems for generalized viscosity explicit methods for nonexpansive mappings in Banach spaces and some applications, Mathematics, 7, 2, 161 (2019) · doi:10.3390/math7020161
[3] Wairojjana, N.; Abdullahi, M. S.; Pakkaranang, N., Fixed point theorems for Meir-Keeler condensing operators in partially ordered Banach spaces, Thai Journal of Mathematics, 18, 1, 77-93 (2020) · Zbl 1482.47106
[4] Ghorpade, S. R.; Limaye, B. V., A Course in Multivariable Calculus and Analysis (2010), Springer · Zbl 1186.26001 · doi:10.1007/978-1-4419-1621-1
[5] Rockafeller, R. T.; Wets, R. J. B., Variational Analysis (2009), Springer
[6] Galewski, M.; Rădulescu, M., On a global implicit function theorem for locally Lipschitz maps via non-smooth critical point theory, Quaestiones Mathematicae, 41, 4, 515-528 (2018) · Zbl 1393.26012 · doi:10.2989/16073606.2017.1391353
[7] Clarke, F. H.; Ledyaev, Y. S.; Stern, R. J.; Wolenski, P. R., Nonsmooth Analysis and Control Theory (1998), New York: Springer-Verlag, New York · Zbl 1047.49500
[8] Bogachev, V. I.; Mayer-Wolf, E., Some remarks on Rademacher’s theorem in infinite dimensions, Potential Analysis, 5, 1, 23-30 (1996) · Zbl 0848.46026 · doi:10.1007/BF00276694
[9] Gutú, O.; Jaramillo, J. A., Surjection and inversion for locally Lipschitz maps between Banach spaces, Journal of Mathematical Analysis and Applications, 478, 2, 578-594 (2019) · Zbl 1440.47047 · doi:10.1016/j.jmaa.2019.05.044
[10] Jaramillo, J. A.; Lajara, S.; Madiedo, Ó., Inversion of nonsmooth maps between Banach spaces, Set-Valued and Variational Analysis, 27, 4, 921-947 (2019) · Zbl 1433.49021 · doi:10.1007/s11228-018-0499-y
[11] Chen, J., Some new generalizations of critical point theorems for locally Lipschitz functions, Journal of Applied Analysis, 14, 2, 193-208 (2008) · Zbl 1162.58004 · doi:10.1515/JAA.2008.193
[12] Galewski, M.; Repovs, D., Global inversibility of mappings between Banach spaces and applications to nonlinear equations, Electronic Journal of Differential Equations, 25, 87-102 (2018) · Zbl 1447.58015
[13] Chen, P.; Tang, X., Periodic solutions for a differential inclusion problem involving the \(p\left( t\right)\)-Laplacian, Advances in Nonlinear Analysis, 10, 799-815 (2021) · Zbl 1471.34043 · doi:10.1515/anona-2020-0156
[14] Dunford, N.; Schwartz, T., Linear Operators, Part 1: General Theory (1988), New York: A Wiley-Interscience, New York · Zbl 0635.47001
[15] Clarke, F. H., A new approach to Lagrange multipliers, Mathematics of Operations Research, 1, 2, 165-174 (1976) · Zbl 0404.90100 · doi:10.1287/moor.1.2.165
[16] Clarke, F. H., Generalized gradients of Lipschitz functionals, Advances in Mathematics, 40, 1, 52-67 (1981) · Zbl 0463.49017 · doi:10.1016/0001-8708(81)90032-3
[17] Clarke, F. H., Generalized gradients and applications, Transactions of the American Mathematical Society, 205, 247-262 (1975) · Zbl 0307.26012 · doi:10.1090/S0002-9947-1975-0367131-6
[18] Chang, K., Variational methods for non-differentiable functionals and their applications to partial differential equations, Journal of Mathematical Analysis and Applications, 80, 1, 102-129 (1981) · Zbl 0487.49027 · doi:10.1016/0022-247X(81)90095-0
[19] Clarke, F. H., Necessary conditions in optimal control and in the calculus of variations, Progress in Nonlinear Differential Equations and their Applications, 75, 143-156 (2007) · Zbl 1144.49013 · doi:10.1007/978-3-7643-8482-1_11
[20] Imbert, C., Support functions of the Clarke generalized Jacobian and of its plenary hull, Nonlinear Analysis, 49, 8, 1111-1125 (2002) · Zbl 1009.49017 · doi:10.1016/S0362-546X(01)00730-1
[21] Zhong, C., On Ekeland’s variational principle and a minimax theorem, Journal of Mathematical Analysis and Applications, 205, 1, 239-250 (1997) · Zbl 0870.49015 · doi:10.1006/jmaa.1996.5168
[22] Clarke, F. H., On the inverse function theorem, Pacific Journal of Mathematics, 64, 1, 97-102 (1976) · Zbl 0331.26013 · doi:10.2140/pjm.1976.64.97
[23] Dontchev, A. L.; Rockafellar, R. T., Implicit Function Theorem and Solution Mappings: A View from Variational Analysis (2014), Springer Series in Operations Research and Financial Engineering · Zbl 1337.26003 · doi:10.1007/978-1-4939-1037-3
[24] Clarke, F. H., Optimisation and nonsmooth analysis, Classics in Applied Mathematics, 5 (1990) · Zbl 0696.49002
[25] Palais, R. S., Natural operations on differential forms, Transactions of the American Mathematical Society, 92, 1, 125-141 (1959) · Zbl 0092.30802 · doi:10.1090/S0002-9947-1959-0116352-7
[26] Antontsev, S. N.; Rodrigues, J. F., On stationary thermo-rheological viscous flows, Annali Dell’Universita’ Di Ferrara, 52, 1, 19-36 (2006) · Zbl 1117.76004 · doi:10.1007/s11565-006-0002-9
[27] Fan, X. L.; Zhao, D., On the space \(L^{p \left( x\right)}\left( \Omega\right)\) and \(W^{m , p \left( x\right)}\left( \Omega\right)\), Journal of Mathematical Analysis and Applications, 263, 424-446 (2001) · Zbl 1028.46041
[28] Tang, C. L.; Wu, X. P., Periodic solutions for second order systems with not uniformly coercive potential, Journal of Mathematical Analysis and Applications, 259, 2, 386-397 (2001) · Zbl 0999.34039 · doi:10.1006/jmaa.2000.7401
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