Study to the Resonance of $ p $-Laplacian problem with mixed boundary
DOI:
https://doi.org/10.5269/bspm.52640Abstract
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.
References
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2. 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.
3. 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.
4. A. Anane, J. P. Gossez, Strongly nonlinear elliptic problems near resonance a variational approach, Comm. Partial Diff Eqns, 15 (1990), 1141-1159.
5. D. Arcoya, L. Orsina, Landesman-Lazer conditions and quasilinear elliptic equations, Nonlinear Analysis, Theory, Methods and Applications. v.28 N 10 (1997) 1623-1632.
6. P. Drabek, S. B. Robinson, Resonance Problems for the p-Laplacian, Journal of Functional Analysis. 169,(1999) 189-200.
7. 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.
8. G. Li, H. Liu, B. Cheng, Eigenvalue problem for p-Laplacian with mixed boundary conditions, Mathematical Sciences 2013, 7:8
9. J. L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Springer, Berlin, 1972.
10. L. Li, Chun-Lei. Tang, Infinitely many solutions for resonance elliptic systems, C. R. Acad. Sci. Paris, Ser. I 353 (2015) 35–40.
11. 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.
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2022-12-26
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