Anisotropic (p, q) Equation with Partially Concave Terms
Abstract
:1. Introduction
2. Materials and Methods
- (a)
- ⟺.
- (b)
- (resp. , ) ⟺ (resp. , ).
- (c)
- ⟹.
- (d)
- ⟹.
- (e)
- (resp. ) ⟺ (resp. ).
- (a)
- for all ⟹ continuously.
- (b)
- for all ⟹ compactly.
- Bounded (that is, maps bounded sets to bounded sets);
- Continuous and strictly monotone (thus, it is maximal monotone, too);
- Of type , that is, if in and , then in .
“Every sequence such that is bounded and in as has a strongly convergent subsequence.”
- :
- , and , .
- :
- is a Carathéodory function such that
- (i)
- for a.a. , all with and ;
- (ii)
- If , then uniformly for a.a. ;
- (iii)
- There exists such that and for all and
- (iv)
- There exists such that for a.a. , all and uniformly for a.a. .
3. Main Result and Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Gasiński, L.; Makrides, G.; Papageorgiou, N.S. Anisotropic (p, q) Equation with Partially Concave Terms. Symmetry 2024, 16, 1188. https://doi.org/10.3390/sym16091188
Gasiński L, Makrides G, Papageorgiou NS. Anisotropic (p, q) Equation with Partially Concave Terms. Symmetry. 2024; 16(9):1188. https://doi.org/10.3390/sym16091188
Chicago/Turabian StyleGasiński, Leszek, Gregoris Makrides, and Nikolaos S. Papageorgiou. 2024. "Anisotropic (p, q) Equation with Partially Concave Terms" Symmetry 16, no. 9: 1188. https://doi.org/10.3390/sym16091188