Existence of solution to a nonlocal biharmonic problem with dependence on gradient and Laplacian

• Autorzy: Shilpa , Dwivedi Gaurav

Identyfikatory

DOI

10.1515/jaa-2021-2073

• Języki publikacji: EN

Abstrakty

EN

In this article, we prove the existence of a solution to a nonlocal biharmonic equation with nonlinearity depending on the gradient and the Laplacian.We employ an iterative technique based on the mountain pass theorem to prove our result.

Słowa kluczowe

EN

biharmonic operator; gradient dependence; mountain pass theorem; iterative methods

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2022
• Tom: Vol. 28, nr 2
• Strony: 211--218
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Shilpa

• Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Vidya Vihar, Pilani, Jhunjhunu, Rajasthan, 333031, India

autor

Dwivedi Gaurav

• Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Vidya Vihar, Pilani, Jhunjhunu, Rajasthan, 333031, India

• https://orcid.org/0000-0002-3615-4808

Bibliografia

• [1] C. O. Alves, F. J. S. A. Corrêa and T. F. Ma, Positive solutions for a quasilinear elliptic equation of Kirchhoff type, Comput. Math. Appl. 49 (2005), no. 1, 85-93.
• [2] A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.
• [3] D. Averna, D. Motreanu and E. Tornatore, Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence, Appl. Math. Lett. 61 (2016), 102-107.
• [4] H. Bueno, G. Ercole, W. Ferreira and A. Zumpano, Existence and multiplicity of positive solutions for the p-Laplacian with nonlocal coefficient, J. Math. Anal. Appl. 343 (2008), no. 1, 151-158.
• [5] H. Bueno, L. Paes-Leme and H. Rodrigues, Multiplicity of solutions for p-biharmonic problems with critical growth, Rocky Mountain J. Math. 48 (2018), no. 2, 425-442.
• [6] P. C. Carrião, L. F. O. Faria and O. H. Miyagaki, A biharmonic elliptic problem with dependence on the gradient and the Laplacian, Electron. J. Differential Equations 2009 (2009), Paper No. 93.
• [7] N. T. Chung, Existence of positive solutions for a nonlocal problem with dependence on the gradient, Appl. Math. Lett. 41 (2015), 28-34.
• [8] N. T. Chung and P. H. Minh, Kirchhoff type problems involving p-biharmonic operators and critical exponents, J. Appl. Anal. Comput. 7 (2017), no. 2, 659-669.
• [9] F. J. S. A. Corrêa and G. M. Figueiredo, A variational approach for a nonlocal and nonvariational elliptic problem, J. Integral Equations Appl. 22 (2010), no. 4, 549-557.
• [10] D. De Figueiredo, M. Girardi and M. Matzeu, Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques, Differential Integral Equations 17 (2004), no. 1-2, 119-126.
• [11] P. Drábek and M. Ôtani, Global bifurcation result for the p-biharmonic operator, Electron. J. Differential Equations 2001 (2001), Paper No. 48.
• [12] F. Faraci, D. Motreanu and D. Puglisi, Positive solutions of quasi-linear elliptic equations with dependence on the gradient, Calc. Var. Partial Differential Equations 54 (2015), no. 1, 525-538.
• [13] F. Gazzola, H.-C. Grunau and G. Sweers, Polyharmonic Boundary Value Problems: Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains, Lecture Notes in Math. 1991, Springer, Berlin, 2010.
• [14] W. Han and J. Yao, The sign-changing solutions for a class of p-Laplacian Kirchhoff type problem in bounded domains, Comput. Math. Appl. 76 (2018), no. 7, 1779-1790.
• [15] J. Liu, L. Wang and P. Zhao, Positive solutions for a nonlocal problem with a convection term and small perturbations, Math. Methods Appl. Sci. 40 (2017), no. 3, 720-728.
• [16] D. Motreanu and P. Winkert, Existence and asymptotic properties for quasilinear elliptic equations with gradient dependence, Appl. Math. Lett. 95 (2019), 78-84.
• [17] N. S. Papageorgiou, C. Vetro and F. Vetro, Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth, Electron. J. Qual. Theory Differ. Equ. 2018 (2018), Paper No. 18.
• [18] Y. Ru, F. Wang, Y. Wang and T. An, On fourth-order elliptic equations of Kirchhoff type with dependence on the gradient and the Laplacian, J. Funct. Spaces 2018 (2018), Article ID 9857038.
• [19] Y. Sang and Y. Ren, A critical p-biharmonic system with negative exponents, Comput. Math. Appl. 79 (2020), no. 5, 1335-1361.
• [20] W. Wang, p-biharmonic equation with Hardy-Sobolev exponent and without the Ambrosetti-Rabinowitz condition, Electron. J. Qual. Theory Differ. Equ. 2020 (2020), Paper No. 42.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).