Fractional elliptic systems with nonlinearities of arbitrary growth
| dc.contributor.author | Ferreira Leite, Edir Junior | |
| dc.date.accessioned | 2022-06-10T19:38:22Z | |
| dc.date.available | 2022-06-10T19:38:22Z | |
| dc.date.issued | 2017-09-07 | |
| dc.description.abstract | In this article we discuss the existence, uniqueness and regularity of solutions of the following system of coupled semilinear Poisson equations on a smooth bounded domain Ω in ℝn: Asu = vp in Ω Asv = ƒ(u) in Ω u = v = 0 on ∂Ω where s ∈ (0, 1) and As denote spectral fractional Laplace operators. We assume that 1 < p < 2s/n-2s, and the function ƒ is superlinear and with no growth restriction (for example ƒ(r) = re r; thus the system has a nontrivial solution. Another important example is given by ƒ(r) = rq. In this case, we prove that such a system admits at least one positive solution for a certain set of the couple (p, q) below the critical hyperbola 1/p+1 + 1/q+1 = n-2s/n whenever n > 2s. For such weak solutions, we prove an L∞ estimate of Brezis-Kato type and derive the regularity property of the weak solutions. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 20 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Ferreira Leite, E. J. (2017). Fractional elliptic systems with nonlinearities of arbitrary growth. Electronic Journal of Differential Equations, 2017(206), pp. 1-20. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15900 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional elliptic systems | |
| dc.subject | Critical growth | |
| dc.subject | Critical hyperbola | |
| dc.title | Fractional elliptic systems with nonlinearities of arbitrary growth | |
| dc.type | Article |