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Multiplicity results to elliptic problems in $\mathbb{R}^N$
Fourth-order hemivariational inequalities
1. | Department of Science for Engineering and Architecture (Mathematics Section), Engineering Faculty, University of Messina, 98166 - Messina, Italy |
References:
[1] |
Z. Bai and H. Wang, On positive solutions of some nonlinear fourth-order beam equations, J. Math. Anal. Appl., 270 (2002), 357-368.
doi: 10.1016/S0022-247X(02)00071-9. |
[2] |
G. Bonanno and B. Di Bella, A boundary value problem for fourth-order elastic beam equations, J. Math. Anal. Appl., 343 (2008), 1166-1176.
doi: 10.1016/j.jmaa.2008.01.049. |
[3] |
G. Bonanno and B. Di Bella, A fourth-order boundary value problem for a Sturm-Liouville type equation, Appl. Math. Comput., 217 (2010), 3635-3640.
doi: 10.1016/j.amc.2010.10.019. |
[4] |
G. Bonanno and B. Di Bella, Infinitely many solutions for fourth-order elastic beam equations, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 357-368. |
[5] |
G. Bonanno and G. Molica Bisci, Infinitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. Value Probl., 2009, Art. ID 670675, 20 pp. |
[6] |
A. Cabada, J. Á. Cid and L. Sanchez, Positivity and lower and upper solutions for fourth order boundary value problems, Nonlinear Anal., 67 (2007), 1599-1612.
doi: 10.1016/j.na.2006.08.002. |
[7] |
S. Carl, V. K. Le and D. Motreanu, "Nonsmoth Variational Problems and Their Inequalities. Comparison Principles and Applications," Springer Monographs in Mathematics, Springer, New York, 2007. |
[8] |
K. C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl., 80 (1981), 102-129.
doi: 10.1016/0022-247X(81)90095-0. |
[9] |
F. H. Clarke, "Optimization and Nonsmooth Analysis," Second edition, Classics Appl. Math., 5, SIAM, Philadelphia, 1990. |
[10] |
E. De Giorgi, G. Buttazzo and G. Dal Maso, On the lower semicontinuity of certain integral functionals, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 74 (1983), 274-282. |
[11] |
M. R. Grossinho, L. Sanchez and S. A. Tersian, On the solvability of a boundary value problem for a fourth-order ordinary differential equation, Appl. Math. Lett., 18 (2005), 439-444. |
[12] |
T. Gyulov and G. Moroşanu, On a nonsmooth fourth order boundary value problem, Nonlinear Anal., 67 (2007), 2800-2814.
doi: 10.1016/j.na.2006.09.041. |
[13] |
T. Gyulov and G. Moroşanu, On a class of boundary value problems involving the p-biharmonic operator, J. Math. Anal. Appl., 367 (2010), 43-57.
doi: 10.1016/j.jmaa.2009.12.022. |
[14] |
G. Han and Z. Xu, Multiple solutions of some nonlinear fourth-order beam equations, Nonlinear Anal., 68 (2008), 3646-3656.
doi: 10.1016/j.na.2007.04.007. |
[15] |
X.-L. Liu and W.-T. Li, Existence and multiplicity of solutions for fourth-order boundary values problems with three parameters, Math. Comput. Modelling, 46 (2007), 525-534.
doi: 10.1016/j.mcm.2006.11.018. |
[16] |
X.-L. Liu and W.-T. Li, Existence and multiplicity of solutions for fourth-order boundary values problems with parameters, J. Math. Anal. Appl., 327 (2007), 362-375.
doi: 10.1016/j.jmaa.2006.04.021. |
[17] |
S. A. Marano and D. Motreanu, Infinitely many critical points of non-differentiable functions and applications to a Neumann type problem involving the p-Laplacian, J. Differential Equations, 182 (2002), 108-120.
doi: 10.1006/jdeq.2001.4092. |
[18] |
D. Motreanu and P. D. Panagiotopoulos, "Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities," Nonconvex Optim. Appl., 29, Kluwer Academic Publishers, Dordrecht, 1999. |
[19] |
D. Motreanu and V. Rădulescu, "Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems," Nonconvex Optimization and Applications, 67, Kluwer Academic Publishers, Dordrecht, 2003. |
show all references
References:
[1] |
Z. Bai and H. Wang, On positive solutions of some nonlinear fourth-order beam equations, J. Math. Anal. Appl., 270 (2002), 357-368.
doi: 10.1016/S0022-247X(02)00071-9. |
[2] |
G. Bonanno and B. Di Bella, A boundary value problem for fourth-order elastic beam equations, J. Math. Anal. Appl., 343 (2008), 1166-1176.
doi: 10.1016/j.jmaa.2008.01.049. |
[3] |
G. Bonanno and B. Di Bella, A fourth-order boundary value problem for a Sturm-Liouville type equation, Appl. Math. Comput., 217 (2010), 3635-3640.
doi: 10.1016/j.amc.2010.10.019. |
[4] |
G. Bonanno and B. Di Bella, Infinitely many solutions for fourth-order elastic beam equations, NoDEA Nonlinear Differential Equations Appl., 18 (2011), 357-368. |
[5] |
G. Bonanno and G. Molica Bisci, Infinitely many solutions for a boundary value problem with discontinuous nonlinearities, Bound. Value Probl., 2009, Art. ID 670675, 20 pp. |
[6] |
A. Cabada, J. Á. Cid and L. Sanchez, Positivity and lower and upper solutions for fourth order boundary value problems, Nonlinear Anal., 67 (2007), 1599-1612.
doi: 10.1016/j.na.2006.08.002. |
[7] |
S. Carl, V. K. Le and D. Motreanu, "Nonsmoth Variational Problems and Their Inequalities. Comparison Principles and Applications," Springer Monographs in Mathematics, Springer, New York, 2007. |
[8] |
K. C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl., 80 (1981), 102-129.
doi: 10.1016/0022-247X(81)90095-0. |
[9] |
F. H. Clarke, "Optimization and Nonsmooth Analysis," Second edition, Classics Appl. Math., 5, SIAM, Philadelphia, 1990. |
[10] |
E. De Giorgi, G. Buttazzo and G. Dal Maso, On the lower semicontinuity of certain integral functionals, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 74 (1983), 274-282. |
[11] |
M. R. Grossinho, L. Sanchez and S. A. Tersian, On the solvability of a boundary value problem for a fourth-order ordinary differential equation, Appl. Math. Lett., 18 (2005), 439-444. |
[12] |
T. Gyulov and G. Moroşanu, On a nonsmooth fourth order boundary value problem, Nonlinear Anal., 67 (2007), 2800-2814.
doi: 10.1016/j.na.2006.09.041. |
[13] |
T. Gyulov and G. Moroşanu, On a class of boundary value problems involving the p-biharmonic operator, J. Math. Anal. Appl., 367 (2010), 43-57.
doi: 10.1016/j.jmaa.2009.12.022. |
[14] |
G. Han and Z. Xu, Multiple solutions of some nonlinear fourth-order beam equations, Nonlinear Anal., 68 (2008), 3646-3656.
doi: 10.1016/j.na.2007.04.007. |
[15] |
X.-L. Liu and W.-T. Li, Existence and multiplicity of solutions for fourth-order boundary values problems with three parameters, Math. Comput. Modelling, 46 (2007), 525-534.
doi: 10.1016/j.mcm.2006.11.018. |
[16] |
X.-L. Liu and W.-T. Li, Existence and multiplicity of solutions for fourth-order boundary values problems with parameters, J. Math. Anal. Appl., 327 (2007), 362-375.
doi: 10.1016/j.jmaa.2006.04.021. |
[17] |
S. A. Marano and D. Motreanu, Infinitely many critical points of non-differentiable functions and applications to a Neumann type problem involving the p-Laplacian, J. Differential Equations, 182 (2002), 108-120.
doi: 10.1006/jdeq.2001.4092. |
[18] |
D. Motreanu and P. D. Panagiotopoulos, "Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities," Nonconvex Optim. Appl., 29, Kluwer Academic Publishers, Dordrecht, 1999. |
[19] |
D. Motreanu and V. Rădulescu, "Variational and Non-variational Methods in Nonlinear Analysis and Boundary Value Problems," Nonconvex Optimization and Applications, 67, Kluwer Academic Publishers, Dordrecht, 2003. |
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