Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators
Abstract
:1. Introduction
- (M1)
- satisfies , where is a constant.
- (M2)
- There exists such that for any .
- (A1)
- ;
- (A2)
- There exist and such that
- (A3)
- There exists such that
- (A4)
- The map is strictly convex.
2. Preliminaries and Main Result
- (H1)
- satisfies the Carathéodory condition and is radial.
- (H2)
- There exist nonnegative functions and such that
- (H3)
- There exists a constant such that for and for any , where .
- (H4)
- uniformly for all .
- (i)
- for , if , then ;
- (ii)
- for if , then ;
- (iii)
- ;
- (iv)
- ;
- (v)
- is reflexive;
- (vi)
- ;
- (vii)
- if , then .
- (D1)
- .
- (D2)
- (D3)
- as .
- (D4)
- I satisfies the -condition for every ,
3. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Lee, J.I.; Kim, Y.-H. Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators. Mathematics 2020, 8, 128. https://doi.org/10.3390/math8010128
Lee JI, Kim Y-H. Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators. Mathematics. 2020; 8(1):128. https://doi.org/10.3390/math8010128
Chicago/Turabian StyleLee, Jun Ik, and Yun-Ho Kim. 2020. "Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators" Mathematics 8, no. 1: 128. https://doi.org/10.3390/math8010128
APA StyleLee, J. I., & Kim, Y.-H. (2020). Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators. Mathematics, 8(1), 128. https://doi.org/10.3390/math8010128