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Applicable Analysis
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Volume 100, 2021 - Issue 10
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Articles

Existence of solutions for a p(x)-biharmonic problem under Neumann boundary conditions

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Pages 2188-2199 | Received 30 Apr 2019, Accepted 08 Oct 2019, Published online: 18 Oct 2019

References

  • Chen Y, Levine S, Rao M. Variable exponent, linear growth functionals in image processing. SIAM J Appl Math. 2006;66:1383–1406. doi: 10.1137/050624522
  • Ruzicka M. Electrorheological fluids: modeling and mathematical theory. Berlin: Springer; 2000.
  • Zhikov VV. Averaging of functionals of the calculus of variations and elasticity theory. Izv Akad Nauk SSSR Ser Mat. 1986;50(4):675–710. English transl. Math. USSR-Izv. 1987;29(1):33–66.
  • Afrouzi GA, Mirzapour M, Chung NT. Existence and multiplicity of solutions for Kirchhoff type problems involving p(x)-biharmonic operators. Z Anal Anwend. 2014;33:289–303. doi: 10.4171/ZAA/1512
  • Chung NT. Multiple solutions for a class of p(x)-Laplacian problems involving concave–convex nonlinearities. Electron J Qual Theory Differ Equ. 2013;2013(26):1–17. doi: 10.14232/ejqtde.2013.1.26
  • Th Chung N. Some remarks on a class of p(x)-Laplacian robin eigenvalue problems. Mediterranean J Math. 2018;15:147. doi:10.1007/s00009-018-1196-7.
  • Chung NT, Ngo QA. Multiple solutions for a class of quasilinear elliptic equations of p(x)-Laplacian type with nonlinear boundary conditions. Proc Royal Soc Edinburgh Sect A Math. 2010;140(2):259–272. doi: 10.1017/S030821050800070X
  • Rădulescu VD. Nonlinear elliptic equations with variable exponent: old and new. Nonlinear Anal. 2015;121:336–369. doi: 10.1016/j.na.2014.11.007
  • Rădulescu VD, Repovš DD. Partial differential equations with variable exponents: variational methods and qualitative analysis. Monographs and Research Notes in Mathematics, Taylor & Francis, Chapman and Hall/CRC, 2015.
  • Ben Haddouch K, El Allali Z, Ayoujil A, et al. Continuous spectrum of a fourth order eigenvalue problem with variable exponent under Neumann boundary conditions. Ann University Craiova Math Comput Sci Ser. 2015;42(1):52–55.
  • ElAmrouss A, Ourraoui A. Existence of solutions for a boundary problem involving p(x)-biharmonic operator. J Bol Soc Paran Mat. 2013;31(1):179–192. doi: 10.5269/bspm.v31i1.15148
  • Taarabti S, El Allali Z, Ben Hadddouch K. Eigenvalues of the p(x)-biharmonic operator with indefinite weight under Neumann boundary conditions. Bol Soc Paran Mat. 2018;36:195–213. doi: 10.5269/bspm.v36i1.31363
  • Wang X, Tian Y. Existence of multiple solutions for a p(x)-biharmonic equation. J Prog Res Math. 2015;6(1):722–733.
  • Ekeland I. On the variational principle. J Math Anal Appl. 1974;47:324–353. doi: 10.1016/0022-247X(74)90025-0
  • Hsini M, Irzi N, Kefi K. Eigenvalues of some p(x)-biharmonic problems under Neumann boundary conditions. Rocky Mountain J Math. 2018;48(8):16. doi:10.1216/RMJ-2018-48-8-2543.
  • Fan X, Shen J, Zhao D. Sobolev embedding theorems for spaces Wk,p(x)(Ω). J Math Anal Appl. 2001;262:749–760. doi: 10.1006/jmaa.2001.7618
  • Harjulehto P, Hästö P, Le UV, et al. Overview of differential equations with non-standard growth. Nonlinear Anal. 2010;72:4551–4574. doi: 10.1016/j.na.2010.02.033
  • Fan X, Han X. Existence and multiplicity of solutions for p(x)-Laplacian equations in RN. Nonlinear Anal. 2004;59:173–188.
  • Orlicz W. Über konjugierte Exponentenfolgen. Studia Math. 1931;3:200–212. doi: 10.4064/sm-3-1-200-211
  • Mashiyev RA, Ogras S, Yucedag Z, et al. Existence and multiplicity of weak solutions for nonuniformly elliptic equations with non-standard growth condition. Complex Var Elliptic Equ. 2012;57:579–595. doi: 10.1080/17476933.2011.598928
  • Edmunds D, Rakosnik J. Sobolev embeddings with variable exponent. Studia Math. 2000;143:267–293. doi: 10.4064/sm-143-3-267-293
  • Liu W, Zhao P. Existence of positive solutions for p(x)-Laplacian equations in unbounded domains. Nonlinear Anal Theory Methods Appl. 2008;69(10):3358–3371. doi: 10.1016/j.na.2007.09.027
  • Fan XL, Zhao D. On the spaces Lp(x)(Ω) and Wm,p(x)(Ω). J Math Anal Appl. 2001;263:424–446. doi: 10.1006/jmaa.2000.7617
  • Kefi K. p(x)-Laplacian with indefinite weight. Proc Amer Math Soc. 2011;139:4351–4360. doi: 10.1090/S0002-9939-2011-10850-5

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