Abstract
In this paper we study the existence of solutions (Formuala presented) with Apu G (Formuala presented) for the Dirichlet problem where (Formuala presented) is a bounded open set with boundary (Formuala presented) stands for the p—Laplace differential operator, (Formuala presented) denotes the subdifferential (in the sense of convex analysis) of a proper convex and lower semicontinuous function (Formuala presented) and (Formuala presented) is a multivalued map. We prove two existence results: the first one deals with the case where the multivalued map (Formuala presented) is upper semicontinuous with closed convex values and the second one deals with the case when (Formuala presented) is lower semicontinuous with closed (not necessarily convex) values.
| Original language | English |
|---|---|
| Pages (from-to) | 859-877 |
| Number of pages | 19 |
| Journal | Set-Valued and Variational Analysis |
| Volume | 22 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2014 |
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Keywords
- Multivalued perturbations
- Quasilinear elliptic equations
- Strong solutions
- Subdifferential operator
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
- Geometry and Topology
- Numerical Analysis
- Statistics and Probability
Cite this
Existence results for quasilinear elliptic equations with multivalued nonlinear terms. / Otani, Mitsuharu; Staicu, Vasile.
In: Set-Valued and Variational Analysis, Vol. 22, No. 4, 2014, p. 859-877.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Existence results for quasilinear elliptic equations with multivalued nonlinear terms
AU - Otani, Mitsuharu
AU - Staicu, Vasile
PY - 2014
Y1 - 2014
N2 - In this paper we study the existence of solutions (Formuala presented) with Apu G (Formuala presented) for the Dirichlet problem where (Formuala presented) is a bounded open set with boundary (Formuala presented) stands for the p—Laplace differential operator, (Formuala presented) denotes the subdifferential (in the sense of convex analysis) of a proper convex and lower semicontinuous function (Formuala presented) and (Formuala presented) is a multivalued map. We prove two existence results: the first one deals with the case where the multivalued map (Formuala presented) is upper semicontinuous with closed convex values and the second one deals with the case when (Formuala presented) is lower semicontinuous with closed (not necessarily convex) values.
AB - In this paper we study the existence of solutions (Formuala presented) with Apu G (Formuala presented) for the Dirichlet problem where (Formuala presented) is a bounded open set with boundary (Formuala presented) stands for the p—Laplace differential operator, (Formuala presented) denotes the subdifferential (in the sense of convex analysis) of a proper convex and lower semicontinuous function (Formuala presented) and (Formuala presented) is a multivalued map. We prove two existence results: the first one deals with the case where the multivalued map (Formuala presented) is upper semicontinuous with closed convex values and the second one deals with the case when (Formuala presented) is lower semicontinuous with closed (not necessarily convex) values.
KW - Multivalued perturbations
KW - Quasilinear elliptic equations
KW - Strong solutions
KW - Subdifferential operator
UR - http://www.scopus.com/inward/record.url?scp=84921416896&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84921416896&partnerID=8YFLogxK
U2 - 10.1007/s11228-014-0289-0
DO - 10.1007/s11228-014-0289-0
M3 - Article
AN - SCOPUS:84921416896
VL - 22
SP - 859
EP - 877
JO - Set-Valued and Variational Analysis
JF - Set-Valued and Variational Analysis
SN - 1877-0533
IS - 4
ER -