2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
Variational Problems: Trends and Applications
Org: Xinyang Lu (Lakehead University) and Chong Wang (Washington and Lee University)
[PDF]
Org: Xinyang Lu (Lakehead University) and Chong Wang (Washington and Lee University)
[PDF]
- MUSTAFA AVCI, Athabasca University
Existence of solutions for a singular double phase variable exponent problem with $(p(\cdot),q(\cdot))-$ Hardy-type potential [PDF]
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In this work, we study a singular double phase variable exponent problem with $(p(\cdot),q(\cdot))-$ Hardy-type potential. We establish existence results using variational methods and critical point theory adapted to the non-standard growth setting, addressing the technical difficulties arising from the lack of homogeneity, the singular nature of Hardy potentials, and the interplay between variable exponents and phase transitions.
{\bf Keywords.} Singularity; variable exponent; variational approach; critical point theory; Hardy-type potential; double phase operator.
- LI BO, University of California, San Diego
- XINYANG LU, Lakehead University
- JACK TISDELL, McGill University
- TONG ZHANG, Memorial Universiry
Liouville-type theorem for the fractional p-Laplacian inequalties [PDF]
- XINYANG LU, Lakehead University
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This work addresses an open question posed in [Math. Ann. 2022, "Quasilinear Laplace equations and inequalities with fractional orders"]. In the process of resolving this problem, we uncovered a key structural insight. This discovery enables us to establish the existence of solutions for a broad class of fractional p-Laplacian inequalities, extending to cases with logarithmic, exponential, and power-law decay at infinity. (Joint work with Professor Jie Xiao.)