Publication Cover
Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 5
75
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Localization of solutions for semilinear problems with poly-Laplace type operators

&
Pages 985-997 | Received 28 Jan 2023, Accepted 23 May 2023, Published online: 01 Jun 2023

References

  • Precup R. Semilinear problems with poly-Laplace type operators. Proc Rom Acad Ser A. 2022;23:319–328.
  • Nicolescu M. Opera matematică: funcţii poliarmonice. Bucureşti: Ed. Academiei; 1980.
  • Bernis F, Garcia-Azorebo J, Peral I. Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth order. Adv Differ Equ. 1996;1:210–240.
  • Bhakta M. Solutions to semilinear elliptic PDE's with biharmonic operator and singular potential. Electron J Differ Equ. 2016;261:1–17.
  • Cheng X, Feng Z, Wei L. Existence and multiplicity of nontrivial solutions for a semilinear biharmonic equation with weight functions. Discrete Cont Dyn Syst Ser S. 2021;14:3067–3083.
  • Pérez-Llanos M, Primo A. Semilinear biharmonic problems with a singular term. J Differ Equ. 2014;257:3200–3225.
  • Gazzola F, Grunau HC, Sweers G. Polyharmonic boundary value problems. Berlin: Springer; 2009.
  • Zhang Y, Lü Y, Wang N. Existence of positive solutions of semilinear biharmonic equations. Abstr Appl Anal. 2014;2014:11 p. Article ID 624328.
  • Jungy T, Choi QH. Applications of topological methods to the semilinear biharmonic problem with different powers. Korean J Math. 2017;25:455–468.
  • Wei G, Zeng L. Estimates for eigenvalues of Poly-Harmonic operators. Adv Nonlinear Stud. 2016;16:31–44.
  • Yolcu SY, Yolcu T. Eigenvalue bounds for the poly-harmonic operators. Illinois J Math. 2014;58:847–865.
  • Cheng QM, Qi X, Wei G. A lower bound for eigenvalues of the poly-Laplace with arbitrary order. Pacific J Math. 2013;262:35–47.
  • Precup R. Abstract weak Harnack inequality, multiple fixed points and p-Laplace equations. J Fixed Point Theory Appl. 2012;12:193–206.
  • Precup R. Compression-expansion fixed point theorems in two norms. Ann Tiberiu Popoviciu Semin Funct Equ Approx Convexity. 2005;3:157–163.
  • O'Regan D, Precup R. Compression-expansion fixed point theorem in two norms and applications. J Math Anal Appl. 2005;309:383–391.
  • Precup R. Moser-Harnack inequality, Krasnosel'skiǐ type fixed point theorems in cones and elliptic problems. Topol Methods Nonlinear Anal. 2012;40:301–313.
  • Precup R. Critical point theorems in cones and multiple positive solutions of elliptic problems. Nonlinear Anal. 2012;75:834–851.
  • Jost J. Partial differential equations. New York: Springer; 2007.
  • Azizieh C, Clement P. A priori estimates and continuation methods for positive solutions of p-Laplace equations. J Differ Equ. 2002;179:213–245.
  • Brezis H. Functional analysis, Sobolev spaces and partial differential equations. New York: Springer; 2011.
  • Precup R. Linear and semilinear partial differential equations. Berlin: De Gruyter; 2013.
  • Herlea DR. Positive solutions for second-order boundary-value problems with phi-Laplacian. Addendum Electron J Differ Equ. 2016;51:1–12.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.