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One-dimensional nonlinear boundary value problems with variable exponent
Quasilinear elliptic equations with measures and multi-valued lower order terms
Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle, Germany |
$Au + G(\cdot,u) \ni f,$ |
$A$ |
$f\in \mathcal M_b(\Omega)$ |
$\Omega\subset \mathbb R^N$ |
$s\mapsto G(\cdot,s)$ |
$s\mapsto \partial j(\cdot,s)$ |
$s\mapsto j(\cdot,s)$ |
References:
[1] |
J. Appell, E. De Pascale, H.T. Nguyen and P.P. Zabrejko,
Multivalued superpositions, Dissertationes Mathematicae, 345 (1995), 1-97.
|
[2] |
L. Boccardo, Some nonlinear Dirichlet problems in L1 involving lower order terms in divergence form, Progress in Elliptic and Parabolic Partial Differential Equations (Capri, 1994),
43–57, Pitman Res. Notes Math. Ser. , 350, Longman, Harlow, 1996. |
[3] |
L. Boccardo and T. Gallouët,
Non-linear elliptic and parabolic equations involving measure data, Journal of Functional Analysis, 87 (1989), 149-169.
doi: 10.1016/0022-1236(89)90005-0. |
[4] |
S. Carl and V.K. Le,
Existence results for hemivariational inequalities with measures, Applicable Analysis, 86 (2007), 735-753.
doi: 10.1080/00036810701397796. |
[5] |
S. Carl and V.K. Le,
Elliptic inequalities with multi-valued operators: Existence, comparison and related variational-hemivariational type inequalities, Nonlinear Analysis: Theory, Methods & Applications, 121 (2015), 130-152.
doi: 10.1016/j.na.2014.10.033. |
[6] |
S. Carl, V. K. Le and D. Motreanu,
Nonsmooth Variational Problems and Their Inequalities Springer Monograph in Mathematics, Springer, New York, 2007.
doi: 10.1007/978-0-387-46252-3. |
[7] |
G. Dal Maso, F. Murat, L. Orsina and A. Prignet,
Renormalized solutions of elliptic equations with general measure data, nnali della Scuola Normale Superiore di Pisa -Classe di Scienze, 28 (1999), 741-808.
|
[8] |
J. J. Duistermaat and J. A. C. Kolk,
Distributions: Theory and Applications Birkhäuser, Boston, 2010.
doi: 10.1007/978-0-8176-4675-2. |
[9] |
J. Leray and J.-L. Lions,
Quelques résultats de Višik sur les problémes elliptiques non linéaires par les méthodes de Minty-Browder, Bulletin de la Société Mathématique de France, 93 (1965), 97-107.
|
[10] |
Z. Naniewicz and P. D. Panagiotopoulos,
Mathematical Theory of Hemivariational Inequalities and Applications Marcel Dekker, Inc. , New York, Basel, Hong Kong, 1995. |
[11] |
A. C. Ponce, Selected problems on elliptic equations involving measures, preprint, arXiv:1204.0668v2. |
[12] |
M. M. Rao,
Measure Theory and Integration Marcel Dekker, Inc. , New York, Basel, 2004. |
[13] |
R. E. Showalter,
Monotone Operators in Banach Space and Nonlinear Partial Differential Equations American Mathematical Society, Providence, RI, 1997. |
[14] |
I. I. Vrabie,
Compactness Methods for Nonlinear Evolutions Pitman Monographs and Surveys in Pure and Applied Mathematikcs, 75 2nd edition, Longman, New York, 1995. |
show all references
References:
[1] |
J. Appell, E. De Pascale, H.T. Nguyen and P.P. Zabrejko,
Multivalued superpositions, Dissertationes Mathematicae, 345 (1995), 1-97.
|
[2] |
L. Boccardo, Some nonlinear Dirichlet problems in L1 involving lower order terms in divergence form, Progress in Elliptic and Parabolic Partial Differential Equations (Capri, 1994),
43–57, Pitman Res. Notes Math. Ser. , 350, Longman, Harlow, 1996. |
[3] |
L. Boccardo and T. Gallouët,
Non-linear elliptic and parabolic equations involving measure data, Journal of Functional Analysis, 87 (1989), 149-169.
doi: 10.1016/0022-1236(89)90005-0. |
[4] |
S. Carl and V.K. Le,
Existence results for hemivariational inequalities with measures, Applicable Analysis, 86 (2007), 735-753.
doi: 10.1080/00036810701397796. |
[5] |
S. Carl and V.K. Le,
Elliptic inequalities with multi-valued operators: Existence, comparison and related variational-hemivariational type inequalities, Nonlinear Analysis: Theory, Methods & Applications, 121 (2015), 130-152.
doi: 10.1016/j.na.2014.10.033. |
[6] |
S. Carl, V. K. Le and D. Motreanu,
Nonsmooth Variational Problems and Their Inequalities Springer Monograph in Mathematics, Springer, New York, 2007.
doi: 10.1007/978-0-387-46252-3. |
[7] |
G. Dal Maso, F. Murat, L. Orsina and A. Prignet,
Renormalized solutions of elliptic equations with general measure data, nnali della Scuola Normale Superiore di Pisa -Classe di Scienze, 28 (1999), 741-808.
|
[8] |
J. J. Duistermaat and J. A. C. Kolk,
Distributions: Theory and Applications Birkhäuser, Boston, 2010.
doi: 10.1007/978-0-8176-4675-2. |
[9] |
J. Leray and J.-L. Lions,
Quelques résultats de Višik sur les problémes elliptiques non linéaires par les méthodes de Minty-Browder, Bulletin de la Société Mathématique de France, 93 (1965), 97-107.
|
[10] |
Z. Naniewicz and P. D. Panagiotopoulos,
Mathematical Theory of Hemivariational Inequalities and Applications Marcel Dekker, Inc. , New York, Basel, Hong Kong, 1995. |
[11] |
A. C. Ponce, Selected problems on elliptic equations involving measures, preprint, arXiv:1204.0668v2. |
[12] |
M. M. Rao,
Measure Theory and Integration Marcel Dekker, Inc. , New York, Basel, 2004. |
[13] |
R. E. Showalter,
Monotone Operators in Banach Space and Nonlinear Partial Differential Equations American Mathematical Society, Providence, RI, 1997. |
[14] |
I. I. Vrabie,
Compactness Methods for Nonlinear Evolutions Pitman Monographs and Surveys in Pure and Applied Mathematikcs, 75 2nd edition, Longman, New York, 1995. |
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