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A DC programming approach for sensor network localization with uncertainties in anchor positions
A class of quasilinear elliptic hemivariational inequality problems on unbounded domains
1. | Department of Mathematics, Soochow University, Suzhou 215006, China, China |
2. | Department of Mathematics, Soochow University, Suzhou, 215006 |
References:
[1] |
C. R. Chen and S. J. Li, Semicontinuity of the solution set map to a set-valued weak vector variational inequality, J. Ind. Manag. Optim., 3 (2007), 519-528.
doi: 10.3934/jimo.2007.3.519. |
[2] |
F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley-interscience, New York, 1983. |
[3] |
Z. Dályay and C. Varga, An existence result for hemivariational inequalities, Electronic J. Differential Equations, 2004 (2004), 1-17. |
[4] |
K. Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann., 142 (1961), 305-310. |
[5] |
F. Faraci, A. Iannizzotto, P. Kupán and C. Varga, Existence and multiplicity results for hemivariational inequalities with two parameters, Nonlinear Anal., 67 (2007), 2654-2669.
doi: 10.1016/j.na.2006.09.030. |
[6] |
M. Filippakis, L. Gasinski and N. S. Papageorgiou, A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential, Nonlinear Anal., 61 (2005), 61-75.
doi: 10.1016/j.na.2004.11.012. |
[7] |
M. Filippakis, L. Gasinski and N. S. Papageorgiou, Nontrivial solutions for resonant hemivariational inequalities, J. Global Optim., 34 (2006), 317-337.
doi: 10.1007/s10898-005-4388-1. |
[8] |
L. Gasinski and N. S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, Chapman and Hall/CRC, New York}, 2005. |
[9] |
F. Gazzola and V. Rădulescu, A nonsmooth critical point theory approach to some nonlinear elliptic equations in $\mathbb{R}^N2$, Differential Integral Equations, 13 (2000), 47-60. |
[10] |
D. Goeleven, D. Motreanu, Y. Dumont and M. Rochdi, Variational and Hemivariational Inequalities: Theory, Methods and Applications, Vol. I. Unilateral analysis and unilateral mechanics. Nonconvex Optimization and its Applications, 69. Kluwer Academic Publishers, Boston, MA, 2003. |
[11] |
S. C. Hu and N. S. Papageorgiou, Positive solutions for nonlinear hemivariational inequalities, J. Math. Anal. Appl., 310 (2005), 161-176.
doi: 10.1016/j.jmaa.2005.01.051. |
[12] |
X. X. Huang and X. Q. Yang, Levitin-Polyak well-posedness in generalized variational inequality problems with functional constraints, J. Ind. Manag. Optim., 3 (2007), 671-684.
doi: 10.3934/jimo.2007.3.671. |
[13] |
Y. S. Huang, Positive solutions of quasilinear elliptic equations, Topol. Meth. Nonl. Anal., 12 (1998), 91-107. |
[14] |
Y. S. Huang and Y. Y. Zhou, Multiple solutions for a class of nonlinear elliptic problems with a p-Laplacian type operator, Nonlinear Anal., 72 (2010), 3388-3395.
doi: 10.1016/j.na.2009.12.020. |
[15] |
A. Kristály, Multiplicity results for an eigenvalue problem for hemivariational inequalities, Set-Valued Analysis, 13 (2005), 85-103.
doi: 10.1007/s11228-004-6565-7. |
[16] |
A. Kristály, C. Varga and V. Varga, A nonsmooth principle of symmetric criticality and variational-hemivariational inequalities in strip-like domains, J. Math. Anal. Appl., 325 (2007), 975-986.
doi: 10.1016/j.jmaa.2006.02.062. |
[17] |
S. J. Li and Z. M. Fang, On the stability of a dual weak vector variational inequality problem, J. Ind. Manag. Optim., 4 (2008), 155-165.
doi: 10.3934/jimo.2008.4.155. |
[18] |
H. Lisei, A. E. Molnr and C. Varga, On a class of inequality problems with lack of compactness, J. Math. Anal. Appl., 378 (2011), 741-748.
doi: 10.1016/j.jmaa.2010.12.041. |
[19] |
Z. H. Liu and D. Motreanu, A class of variational-hemivariational inequalities of elliptic type, Nonlinearity, 23 (2010), 1741-1752.
doi: 10.1088/0951-7715/23/7/012. |
[20] |
I. I. Mezei and L. Săplăcan, Existence result and applications for general variational-hemivariational inequalities on unbounded domains, Electronic J. Differential Equations, 2009 (2009), 1-10. |
[21] |
D. Motreanu and P. D. Panagiotopoulos, Minimax Theorem and Qualitative Properties of the Solutions of Hemivariational Inequalities, Nonconvex Optimization and its Applications, 29. Kluwer Academic Publishers, Dordrecht, 1999. |
[22] |
D. Motreanu and V. Radulescu, Variational and Non-Variational Methods in Nonlinear Analysis and Boundary Value Problems, Kluwer Academic Publishers, Boston, 2003. |
[23] |
P. D. Panagiotopoulos, Hemivariational Inequalities, Applications in Mechanics and Engineering, Springer, Berlin, 1993.
doi: 10.1007/978-3-642-51677-1. |
[24] |
L. Scrimali, Mixed behavior network equilibria and quasi-variational inequalities, J. Ind. Manag. Optim., 5 (2009), 363-379.
doi: 10.3934/jimo.2009.5.363. |
[25] |
A. Szulkin and M. Willem, Eigenvalue problems with indefinite weight, Studia. Math., 135 (1999), 191-201. |
[26] |
R. Xiao and Y. Y. Zhou, Multiple solutions for a class of semilinear elliptic variational inclusion problems, J. Ind. Manag. Optim., 7 (2011), 991-1002.
doi: 10.3934/jimo.2011.7.991. |
show all references
References:
[1] |
C. R. Chen and S. J. Li, Semicontinuity of the solution set map to a set-valued weak vector variational inequality, J. Ind. Manag. Optim., 3 (2007), 519-528.
doi: 10.3934/jimo.2007.3.519. |
[2] |
F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley-interscience, New York, 1983. |
[3] |
Z. Dályay and C. Varga, An existence result for hemivariational inequalities, Electronic J. Differential Equations, 2004 (2004), 1-17. |
[4] |
K. Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann., 142 (1961), 305-310. |
[5] |
F. Faraci, A. Iannizzotto, P. Kupán and C. Varga, Existence and multiplicity results for hemivariational inequalities with two parameters, Nonlinear Anal., 67 (2007), 2654-2669.
doi: 10.1016/j.na.2006.09.030. |
[6] |
M. Filippakis, L. Gasinski and N. S. Papageorgiou, A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential, Nonlinear Anal., 61 (2005), 61-75.
doi: 10.1016/j.na.2004.11.012. |
[7] |
M. Filippakis, L. Gasinski and N. S. Papageorgiou, Nontrivial solutions for resonant hemivariational inequalities, J. Global Optim., 34 (2006), 317-337.
doi: 10.1007/s10898-005-4388-1. |
[8] |
L. Gasinski and N. S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, Chapman and Hall/CRC, New York}, 2005. |
[9] |
F. Gazzola and V. Rădulescu, A nonsmooth critical point theory approach to some nonlinear elliptic equations in $\mathbb{R}^N2$, Differential Integral Equations, 13 (2000), 47-60. |
[10] |
D. Goeleven, D. Motreanu, Y. Dumont and M. Rochdi, Variational and Hemivariational Inequalities: Theory, Methods and Applications, Vol. I. Unilateral analysis and unilateral mechanics. Nonconvex Optimization and its Applications, 69. Kluwer Academic Publishers, Boston, MA, 2003. |
[11] |
S. C. Hu and N. S. Papageorgiou, Positive solutions for nonlinear hemivariational inequalities, J. Math. Anal. Appl., 310 (2005), 161-176.
doi: 10.1016/j.jmaa.2005.01.051. |
[12] |
X. X. Huang and X. Q. Yang, Levitin-Polyak well-posedness in generalized variational inequality problems with functional constraints, J. Ind. Manag. Optim., 3 (2007), 671-684.
doi: 10.3934/jimo.2007.3.671. |
[13] |
Y. S. Huang, Positive solutions of quasilinear elliptic equations, Topol. Meth. Nonl. Anal., 12 (1998), 91-107. |
[14] |
Y. S. Huang and Y. Y. Zhou, Multiple solutions for a class of nonlinear elliptic problems with a p-Laplacian type operator, Nonlinear Anal., 72 (2010), 3388-3395.
doi: 10.1016/j.na.2009.12.020. |
[15] |
A. Kristály, Multiplicity results for an eigenvalue problem for hemivariational inequalities, Set-Valued Analysis, 13 (2005), 85-103.
doi: 10.1007/s11228-004-6565-7. |
[16] |
A. Kristály, C. Varga and V. Varga, A nonsmooth principle of symmetric criticality and variational-hemivariational inequalities in strip-like domains, J. Math. Anal. Appl., 325 (2007), 975-986.
doi: 10.1016/j.jmaa.2006.02.062. |
[17] |
S. J. Li and Z. M. Fang, On the stability of a dual weak vector variational inequality problem, J. Ind. Manag. Optim., 4 (2008), 155-165.
doi: 10.3934/jimo.2008.4.155. |
[18] |
H. Lisei, A. E. Molnr and C. Varga, On a class of inequality problems with lack of compactness, J. Math. Anal. Appl., 378 (2011), 741-748.
doi: 10.1016/j.jmaa.2010.12.041. |
[19] |
Z. H. Liu and D. Motreanu, A class of variational-hemivariational inequalities of elliptic type, Nonlinearity, 23 (2010), 1741-1752.
doi: 10.1088/0951-7715/23/7/012. |
[20] |
I. I. Mezei and L. Săplăcan, Existence result and applications for general variational-hemivariational inequalities on unbounded domains, Electronic J. Differential Equations, 2009 (2009), 1-10. |
[21] |
D. Motreanu and P. D. Panagiotopoulos, Minimax Theorem and Qualitative Properties of the Solutions of Hemivariational Inequalities, Nonconvex Optimization and its Applications, 29. Kluwer Academic Publishers, Dordrecht, 1999. |
[22] |
D. Motreanu and V. Radulescu, Variational and Non-Variational Methods in Nonlinear Analysis and Boundary Value Problems, Kluwer Academic Publishers, Boston, 2003. |
[23] |
P. D. Panagiotopoulos, Hemivariational Inequalities, Applications in Mechanics and Engineering, Springer, Berlin, 1993.
doi: 10.1007/978-3-642-51677-1. |
[24] |
L. Scrimali, Mixed behavior network equilibria and quasi-variational inequalities, J. Ind. Manag. Optim., 5 (2009), 363-379.
doi: 10.3934/jimo.2009.5.363. |
[25] |
A. Szulkin and M. Willem, Eigenvalue problems with indefinite weight, Studia. Math., 135 (1999), 191-201. |
[26] |
R. Xiao and Y. Y. Zhou, Multiple solutions for a class of semilinear elliptic variational inclusion problems, J. Ind. Manag. Optim., 7 (2011), 991-1002.
doi: 10.3934/jimo.2011.7.991. |
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