Positive solutions to nonlinear inclusion problems in Orlicz–Sobolev spaces

References

• Liu Z, Motreanu D. Inclusion problems via subsolution–supersolution method with applications to hemivariational inequalities. Appl Anal. 2018;97:1454–1465. doi: 10.1080/00036811.2017.1408076
   Web of Science ®Google Scholar
• Zeng S, Liu Z, Migórski S. Positive solutions to nonlinear nonhomogeneous inclusion problems with dependence on the gradient. J Math Anal Appl. 2018;463:432–448. doi: 10.1016/j.jmaa.2018.03.033
   Web of Science ®Google Scholar
• Le VK. On variational and quasi-variational inequalities with multivalued lower order terms and convex functionals. Nonlinear Anal. 2014;94:12–31. doi: 10.1016/j.na.2013.07.034
   Web of Science ®Google Scholar
• Carl S, Le VK. Elliptic inequalities with multi-valued operators: existence, comparison and related variational-hemivariational type inequalities. Nonlinear Anal. 2015;121:130–152. doi: 10.1016/j.na.2014.10.033
   Web of Science ®Google Scholar
• Dong G, Fang X. Variational inequalities with multivalued lower order terms and convex functionals in Orlicz–Sobolev spaces. J Funct Spaces. 2015;2015: 10 pp.
   Web of Science ®Google Scholar
• Carl S. Barrier solutions of elliptic variational inequalities. Nonlinear Anal. 2015;26:75–92. doi: 10.1016/j.nonrwa.2015.04.004
   Web of Science ®Google Scholar
• Kaufmann U, Milne L. Positive solutions of generalized nonlinear logistic equations via sub-super solutions. J Math Anal Appl. 2019;471:653–670. doi: 10.1016/j.jmaa.2018.11.001
   Web of Science ®Google Scholar
• Carl S, Le VK, Motreanu D. Nonsmooth variational problems and their inequalities: comparison principles and applications. New York (NY): Springer; 2007.
   Google Scholar
• Dong G, Shi Z. An existence theorem for weak solutions for a class of elliptic partial differential systems in Orlicz spaces. Nonlinear Anal. 2008;68:1037–1042. doi: 10.1016/j.na.2006.12.004
   Web of Science ®Google Scholar
• Dong G. An existence theorem for weak solutions for a class of elliptic partial differential systems in general Orlicz–Sobolev spaces. Nonlinear Anal. 2008;69:2049–2057. doi: 10.1016/j.na.2007.07.043
   Web of Science ®Google Scholar
• Dong G. Elliptic equations with measure data in Orlicz spaces. Electron J Differ Eq. 2008;76: 10 pp.
   Google Scholar
• Faria LFO, Miyagaki OH, Tanaka M. Existence of a positive solution for problems with (p,q)-Laplacian and convection term in RN. Bound Value Probl. 2016;158: 20 pp.
   Google Scholar
• Papageorgiou NS, Rădulescu VD, Repovš DD. Nonlinear elliptic inclusions with unilateral constraint and dependence on the gradient. Appl Math Optim. 2018;78:1–23. doi: 10.1007/s00245-016-9392-y
   Web of Science ®Google Scholar
• Chipot M, Guesmia S, Harkat S. On the minimal solution for some variational inequalities. J Differ Eq. 2019;266:493–525. doi: 10.1016/j.jde.2018.07.052
   Web of Science ®Google Scholar
• Adams RA, Fournier JJF. Sobolev spaces. 2nd ed. New York (NY): Academic Press; 2003.
   Google Scholar
• Krasnosel'skiĭ MA, Rutickiĭ YB. Convex functions and Orlicz spaces. Groningen: Noordhoff; 1961. (translated by Boron LF).
   Google Scholar
• Chen ST. Geometry of Orlicz spaces [Dissertationes Math. 356]. Warszawa: Instytut Matematyczny PAN; 1996.
   Google Scholar
• Gossez J. Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients. Trans Amer Math Soc. 1974;190:163–205. doi: 10.1090/S0002-9947-1974-0342854-2
   Web of Science ®Google Scholar
• Chlebicka I. A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces. Nonlinear Anal. 2018;175:1–27. doi: 10.1016/j.na.2018.05.003
   Web of Science ®Google Scholar
• Browder FE, Hess P. Nonlinear mappings of monotone type in Banach spaces. J Funct Anal. 1972;11:251–294. doi: 10.1016/0022-1236(72)90070-5
   Google Scholar
• Zeidler E. Nonlinear functional analysis and its applications. II/B: Nonlinear monotone operators. New York (NY): Springer-Verlag; 1990. (translated by Zeidler E and Boront LF).
   Google Scholar
• Fan X. Differential equations of divergence form in Musielak–Sobolev spaces and a sub-supersolution method. J Math Anal Appl. 2012;386:593–604. doi: 10.1016/j.jmaa.2011.08.022
   Web of Science ®Google Scholar
• Dong G, Fang X. The sub-supersolution method and extremal solutions of quasilinear elliptic equations in Orlicz–Sobolev spaces. J Funct Spaces. 2018;2018: 7 pp.
   Web of Science ®Google Scholar
• Dong G, Fang X. Existence results for some nonlinear elliptic equations with measure data in Orlicz–Sobolev spaces. Bound Value Probl. 2015;18: 22 pp.
   Google Scholar
• Landes R. On Galerkin's method in the existence theory of quasilinear elliptic equations. J Funct Anal. 1980;39:123–148. doi: 10.1016/0022-1236(80)90009-9
   Web of Science ®Google Scholar
• Gasinski L, Papageorgiou NS. Exercises in analysis: part 1. New York (NY): Springer; 2014.
   Google Scholar
• García-Huidobro M, Le V, Manásevich R, et al. On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz–Sobolev space setting. Nonlinear Differ Eq Appl. 1999;6:207–225. doi: 10.1007/s000300050073
   Web of Science ®Google Scholar
• Gasiński L, Papageorgiou NS. Nonlinear analysis. Boca Raton (FL): Chapman & Hall/CRC; 2006.
   Google Scholar
• Clarke FH. Optimization and nonsmooth analysis. New York (NY): Wiley; 1983.
   Google Scholar