Low perturbations of p-biharmonic equations with competing nonlinearities

References

• Lazer AC, McKenna PJ. Large-amplitude periodic oscillations in suspension bridge: some new connections with nonlinear analysis. SIAM Rev. 1990;32:537–578. doi: 10.1137/1032120
   Web of Science ®Google Scholar
• McKenna PJ, Walter W. Nonlinear oscillation in a suspension bridge. Arch Ration Mech Anal. 1987;98:167–177. doi: 10.1007/BF00251232
   Web of Science ®Google Scholar
• McKenna PJ, Walter W. Traveling waves in a suspension bridge. SIAM J Appl Math. 1990;50:703–715. doi: 10.1137/0150041
   Web of Science ®Google Scholar
• Alsaedi R, Radulescu VD. Generalized biharmonic problems with variable exponent and Navier boundary condition. Electr J Differ Equ Conf. 2018;25:27–37. Two nonlinear days in Urbino 2017.
   Google Scholar
• Ben Ali K, Bezzarga M, Ghanmi A, et al. Existence of positive solution for Kirchhoff problems. Complex Anal Oper Theory. 2019;13(1):115–126. doi: 10.1007/s11785-017-0709-x
   Web of Science ®Google Scholar
• Boureanu MM, Radulescu V, Repovs D. On a p(.)-biharmonic problem with no-flux boundary condition. Comput Math Appl. 2016;72:2505–2515. doi: 10.1016/j.camwa.2016.09.017
   Web of Science ®Google Scholar
• El Khalil A, Laghzal M, Morchid Alaoui MD, et al. Eigenvalues for a class of singular problems involving p(x)-biharmonic operator and q(x)-Hardy potential. Adv Nonlinear Anal. 2020;9(1):1130–1144. doi: 10.1515/anona-2020-0042
   Google Scholar
• Ji C, Wang WH. On the p-biharmonic equation involving concave-convex nonlinearities and sign-changing weight function. Electron J Qual Theory Differ Equ. 2012;2:1–17.
   Google Scholar
• Kefi K, Radulescu VD. On a p(x)-biharmonic problem with singular weights. Zeitschrift für angewandte Mathematik und Physik (ZAMP). 2017;68:68–80. doi: 10.1007/s00033-017-0816-6
   Google Scholar
• Papageorgiou NS, Radulescu VD, Repovs D. Asymmetric Robin problems with indefinite potential and concave terms. Adv Nonlinear Stud. 2019;19(1):69–87. doi: 10.1515/ans-2018-2022
   Web of Science ®Google Scholar
• Papageorgiou NS, Radulescu VD, Repovs D. Positive solutions for nonlinear parametric singular Dirichlet problems. Bull Math Sci. 2019;9(3):1950011, 21 pp. doi: 10.1142/S1664360719500115
   Web of Science ®Google Scholar
• Papageorgiou NS, Radulescu VD, Repovs D. Nonlinear analysis – theory and methods. Cham: Springer; 2019. (Springer Monographs in Mathematics).
   Google Scholar
• Papageorgiou NS, Zhang C. Noncoercive resonant (p,2)-equations with concave terms. Adv Nonlinear Anal. 2020;9(1):228–249. doi: 10.1515/anona-2018-0175
   Google Scholar
• Radulescu VD, Repovs D. Combined effects for non-autonomous singular biharmonic problems. Discrete and Continuous Dynamical Systems – S (in press). doi:10.3934/dcdss.2020158
   Google Scholar
• Sun J, Chu J, Wu TF. Existence and multiplicity of nontrivial solutions for some biharmonic equations with p-Laplacian. J Differ Equ. 2017;262:945–977. doi: 10.1016/j.jde.2016.10.001
   Web of Science ®Google Scholar
• Sun J, Wu TF. Existence of nontrivial solutions for a biharmonic equation with p-Laplacian and singular sign-changing potential. Appl Math Lett. 2017;66:61–67. doi: 10.1016/j.aml.2016.11.001
   Web of Science ®Google Scholar
• Ghanmi A. Existence of nonnegative solutions for a class of fractional p-Laplacian problems. Nonlinear Stud. 2015;22(3):373–379.
   Google Scholar
• Ghanmi A. Multiplicity of nontrivial solutions of a class of fractional p-Laplacian problem. Z Anal Anwend. 2015;34(3):309–319. doi: 10.4171/ZAA/1541
   Web of Science ®Google Scholar
• Ghanmi A, Saoudi K. A multiplicity results for a singular problem involving the fractional p-Laplacian operator. Complex Variables Elliptic Equ. 2016;61(9):1199–1216. doi: 10.1080/17476933.2016.1154548
   Web of Science ®Google Scholar
• Giri RK, Choudhuri D, Pradhan S. A study on elliptic PDE involving p-harmonic and p-biharmonic operator with steep potential well. Mathematicki Vesnik. 2018;70(2):147–154.
   Web of Science ®Google Scholar
• Dràbek P, Pohozaev SI. Positive solutions for the p-Laplacian: application of the fibering method. Proc Roy Soc Edinburgh Sect A. 1997;127:703–726. doi: 10.1017/S0308210500023787
   Google Scholar
• Wu TF. On semilinear elliptic equations involving concave-convex nonlinearities and sign-changing weight function. J Math Anal. 2006;318:253–270. doi: 10.1016/j.jmaa.2005.05.057
   Web of Science ®Google Scholar
• Liu L, Chen C. Infinitely many solutions for p-biharmonic equation with general potential and concave-convex nonlinearity in Rn. Bound Value Prob. 2016;2016:6. doi: 10.1186/s13661-015-0510-6
   Google Scholar
• Brezis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. Proc Amer Math Soc. 1983;88:486–490. doi: 10.2307/2044999
   Web of Science ®Google Scholar
• Saiedinezhad S. Existence of solutions to biharmonic equations with sing changing coefficients. Electron J Differ Equ. 2018;2018(99):1–9.
   Google Scholar
• Xu L, Chen H. Existence of positive ground solutions for biharmonic equations via Pohoz˜aev–Nehari manifold. Topol Methods Nonlinear Anal. 2018;52(2):541–560.
   Web of Science ®Google Scholar