Nontrivial solutions for a general p(x)-Laplacian Robin problem
DOI:
https://doi.org/10.5269/bspm.62755Resumo
We establish the existence of multiple nontrivial solutions for a class of $p(x)$-Laplacian Robin problem. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with
adequate variational methods and a variant of the Mountain Pass lemma.
Referências
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2. M. Allaoui, A. R. El Amrouss, F. Kissi and A. Ourraoui, Existence and multiplicity of solutions for a Robin problem, J. Math. Comput. Sci., 10 (2014), 163-172.
3. M. Allaoui, A. R. El Amrouss and A. Ourraoui, Existence results for a class of p(x)-Laplacian problems in RN , Comput. Math. Appl., 69 (2015) 582-591.
4. J. Chabrowski and Y. Fu, Existence of solutions for p(x)-Laplacian problems on a bounded domain, J. Math. Anal. Appl. 306 (2005), 604-618.
5. Y. M. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006) 1383-1406.
6. S. G. Dend, Q. Wang and S. J. Cheng,On the p(x)-Laplacian Robin eigenvalue problem, Appl. Math. Comput., 217 (2011), 5643-5649.
7. S. G. Dend, A local mountain pass theorem and applications to a double perturbed p(x)-Laplacian equations, Appl. Math. Comput., 211 (2009), 234-241.
8. S. G. Dend, Positive solutions for Robin problem involving the p(x)-Laplacian, J. Math. Anal. Appl. 360 (2009) 548-560.
9. X. Ding and X. Shi, Existence and multiplicity of solutions for a general p(x)-Laplacian Neumann problem, Nonlinear. Anal., 70(2009), 3713-3720.
10. X. L. Fan, J. S. Shen, D. Zhao, Sobolev embedding theorems for spaces Wk,p(x) , J. Math. Anal. Appl. 262 (2001), 749-760.
11. N. Tsouli, M. Haddaoui and ELM Hssini,Multiple Solution for a Critical p(x)-Kirchhoff Type Equations, Bol. Soc. Paran. Mat.(3s.) v. 38 4 (2020): 197-211.
12. X. L. Fan, D. Zhao, On the spaces Lp(x) and W m,p(x), J. Math. Anal. Appl. 263 (2001), 424-446.
13. X. L. Fan, Q. H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problems, Nonlinear Anal. 52 (2003) 1843-1852.
14. M. Ruzicka, Electrorheological fluids: Modeling and Mathematical Theory, Springer-Verlag, Berlin, 2000.
15. L. L. Wang, Y. H. Fan and W. G. Ge, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator, Nonlinear. Anal., 71 (2009), 4259-4270.
16. V. V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR. Izv. 29 (1987) 33-66.
2. M. Allaoui, A. R. El Amrouss, F. Kissi and A. Ourraoui, Existence and multiplicity of solutions for a Robin problem, J. Math. Comput. Sci., 10 (2014), 163-172.
3. M. Allaoui, A. R. El Amrouss and A. Ourraoui, Existence results for a class of p(x)-Laplacian problems in RN , Comput. Math. Appl., 69 (2015) 582-591.
4. J. Chabrowski and Y. Fu, Existence of solutions for p(x)-Laplacian problems on a bounded domain, J. Math. Anal. Appl. 306 (2005), 604-618.
5. Y. M. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006) 1383-1406.
6. S. G. Dend, Q. Wang and S. J. Cheng,On the p(x)-Laplacian Robin eigenvalue problem, Appl. Math. Comput., 217 (2011), 5643-5649.
7. S. G. Dend, A local mountain pass theorem and applications to a double perturbed p(x)-Laplacian equations, Appl. Math. Comput., 211 (2009), 234-241.
8. S. G. Dend, Positive solutions for Robin problem involving the p(x)-Laplacian, J. Math. Anal. Appl. 360 (2009) 548-560.
9. X. Ding and X. Shi, Existence and multiplicity of solutions for a general p(x)-Laplacian Neumann problem, Nonlinear. Anal., 70(2009), 3713-3720.
10. X. L. Fan, J. S. Shen, D. Zhao, Sobolev embedding theorems for spaces Wk,p(x) , J. Math. Anal. Appl. 262 (2001), 749-760.
11. N. Tsouli, M. Haddaoui and ELM Hssini,Multiple Solution for a Critical p(x)-Kirchhoff Type Equations, Bol. Soc. Paran. Mat.(3s.) v. 38 4 (2020): 197-211.
12. X. L. Fan, D. Zhao, On the spaces Lp(x) and W m,p(x), J. Math. Anal. Appl. 263 (2001), 424-446.
13. X. L. Fan, Q. H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problems, Nonlinear Anal. 52 (2003) 1843-1852.
14. M. Ruzicka, Electrorheological fluids: Modeling and Mathematical Theory, Springer-Verlag, Berlin, 2000.
15. L. L. Wang, Y. H. Fan and W. G. Ge, Existence and multiplicity of solutions for a Neumann problem involving the p(x)-Laplace operator, Nonlinear. Anal., 71 (2009), 4259-4270.
16. V. V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Math. USSR. Izv. 29 (1987) 33-66.
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2024-04-19
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