Study to the Resonance of $ p $-Laplacian problem with mixed boundary
Resumen
In this work, we are interested at the existence of nontrivial solutions for a nonlinear elliptic problems with resonance part and mixed boundary conditions. Our approach is variational and is based on the well known Landesman-Laser type conditions.
Descargas
Citas
G. A. Afrouzi, M. Mirzapour, A. Hadjian, S. Shakeri, Existence of solutions of weak solutions for a semilinear problem with a nonlinear boundary condition, Bulletin of Mathematical Analysis and Applications, Volume 3 Issue 3(2011), Pages 109-114.
C. O. Alves, P. C. Carriao, O. H. Miyagaki, Multiple solutions for a problem with resonance involving the p-laplacian, Abstr. Appl. Anal, volume 3, number 1-2 (1998), 191-210. DOI: https://doi.org/10.1155/S1085337598000517
A. Anane, O. Chakron, B. Karim, A. Zerouli, Existence of solution for a resonant Steklov Problem, Bol.Soc. Paranaense de Mat.(3s) v.27 1 (2009) 87-90. DOI: https://doi.org/10.5269/bspm.v27i1.9070
A. Anane, J. P. Gossez, Strongly nonlinear elliptic problems near resonance a variational approach, Comm. Partial Diff Eqns, 15 (1990), 1141-1159. DOI: https://doi.org/10.1080/03605309908820717
D. Arcoya, L. Orsina, Landesman-Lazer conditions and quasilinear elliptic equations, Nonlinear Analysis, Theory, Methods and Applications. v.28 N 10 (1997) 1623-1632. DOI: https://doi.org/10.1016/S0362-546X(96)00022-3
P. Drabek, S. B. Robinson, Resonance Problems for the p-Laplacian, Journal of Functional Analysis. 169,(1999) 189-200. DOI: https://doi.org/10.1006/jfan.1999.3501
El. M. Hssini, M. Massar, M. Talbi and N. Tsouli, Existence of solutions for a fourth order problem at resonance, Bol. Soc. Paran. Mat. (3s.) v. 32 2 (2014): 133–142. DOI: https://doi.org/10.5269/bspm.v32i2.18216
G. Li, H. Liu, B. Cheng, Eigenvalue problem for p-Laplacian with mixed boundary conditions, Mathematical Sciences 2013, 7:8 DOI: https://doi.org/10.1186/2251-7456-7-8
J. L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer, Berlin, 1972. DOI: https://doi.org/10.1007/978-3-642-65217-2
L. Li, Chun-Lei. Tang, Infinitely many solutions for resonance elliptic systems, C. R. Acad. Sci. Paris, Ser. I 353 (2015) 35–40. DOI: https://doi.org/10.1016/j.crma.2014.10.010
P. H. Rabinowitz, Some minimax theorems and applications to partial differential equations, Nonlinear Analysis: A collection of papers honor of Erich Rothe. Academic press, New York, 1978, pp. 161-177. DOI: https://doi.org/10.1016/B978-0-12-165550-1.50016-1
Derechos de autor 2022 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
