Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator
Abstract
:1. Introduction
2. Preliminaries
3. Main Results
- (a)andthe functionalhas a global minimum inwhich is a critical point (local minimum) ofin.
- (b) If, then,, one of the following two conclusions holds: either
- (b1)has a global minimum, or
- (b2)has a sequence local minimum (critical points) denoted by.
- (c) If, then,, one of the following two conclusions holds: either
- (c1)has a global minimum which is a local minimum of, or
- (c2) has a sequence of pairwise distinct local minimum (critical points) which weakly converges to a global minimum of .
4. Discussion
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Miao, Q. Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator. Mathematics 2019, 7, 756. https://doi.org/10.3390/math7080756
Miao Q. Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator. Mathematics. 2019; 7(8):756. https://doi.org/10.3390/math7080756
Chicago/Turabian StyleMiao, Qing. 2019. "Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator" Mathematics 7, no. 8: 756. https://doi.org/10.3390/math7080756
APA StyleMiao, Q. (2019). Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator. Mathematics, 7(8), 756. https://doi.org/10.3390/math7080756