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Existence of solutions for perturbed fractional p-Laplacian equations.
- Source :
-
Journal of Differential Equations . Jan2016, Vol. 260 Issue 2, p1392-1413. 22p. - Publication Year :
- 2016
-
Abstract
- The purpose of this paper is to investigate the existence of weak solutions for a perturbed nonlinear elliptic equation driven by the fractional p -Laplacian operator as follows: ( − Δ ) p s u + V ( x ) | u | p − 2 u = λ a ( x ) | u | r − 2 u − b ( x ) | u | q − 2 u in R N , where λ is a real parameter, ( − Δ ) p s is the fractional p -Laplacian operator with 0 < s < 1 < p < ∞ , p < r < min { q , p s ⁎ } and V , a , b : R N → ( 0 , ∞ ) are three positive weights. Using variational methods, we obtain nonexistence and multiplicity results for the above-mentioned equations depending on λ and according to the integrability properties of the ratio a q − p / b r − p . Our results extend the previous work of Autuori and Pucci (2013) [5] to the fractional p -Laplacian setting. Furthermore, we weaken one of the conditions used in their paper. Hence the results of this paper are new even in the fractional Laplacian case. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 260
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 110789781
- Full Text :
- https://doi.org/10.1016/j.jde.2015.09.028