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In this paper the authors study the existence of positive radial solutions to the Kirchhoff type problem involving the p-Laplacian [formula] where λ > 0 is a parameter, Ωe = {x ∈ RN : |x| > r0}, r0 > 0, N > p > 1, Δp is the p-Laplacian operator, and f ∈ C([r0,+∞) × [0,+∞) ,R) is a non-decreasing function with respect to its second variable. By using the Mountain Pass Theorem, they prove the existence of positive radial solutions for small values of λ.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
47--66
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- University of Tennessee at Chattanooga, Department of Mathematics, Chattanooga, TN 37403, USA
autor
- Ecole Normale Supérieure, Laboratory of Partial Differential Equations and History of Mathematics, Kouba, Algiers, Algeria
autor
- Ecole Normale Supérieure, Laboratory of Fixed Point Theory and Applications, Kouba, Algiers, Algeria
Bibliografia
- [1] N. Aissaoui, W. Long, Positive solutions for a Kirchhoff equation with perturbed source terms, Acta Math. Scientia 42 (2022), 1817–1830.
- [2] C.O. Alves, F.J.S.A. Corrêa, T.F. Ma, Positive solutions for a quasilinear elliptic equation of Kirchhoff type, Comput. Math. Appl. 49 (2005), 85–93.
- [3] A. Ambrosetti, P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349–381.
- [4] M. Badiale, E. Serra, Semilinear Elliptic Equations for Beginners. Existence Results via the Variational Approach, Universitext, Springer, London, 2011.
- [5] H. Brézis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2010.
- [6] D. Butler, E. Ko, E.K. Lee, R. Shivaji, Positive radial solutions for elliptic equations on exterior domains with nonlinear boundary conditions, Comm. Pure Appl. Anal. 13 (2014), 2713–2731.
- [7] A. Castro, R. Shivaji, Nonnegative solutions for a class of nonpositone problems, Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), 291–302.
- [8] A. Castro, D.G. de Figueiredo, E. Lopera, Existence of positive solutions for a semipositone p-Laplacian problem, Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), 475–482.
- [9] R. Dhanya, Q. Morris, R. Shivaji, Existence of positive radial solutions for superlinear semipositone problems on the exterior of a ball, J. Math. Anal. Appl. 434 (2016), 1533–1548.
- [10] M. Ding, C. Zhang, S. Zhou, Local boundedness and Hölder continuity for the parabolic fractional p-Laplace equations, Calc. Var. Partial Differential Equations 60 (2021), Article no. 38.
- [11] L. Gasinski, N.S. Papageorgiou, Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, Series in Mathematical Analysis and Applications, vol. 8, Chapman & Hall/CRC, Boca Raton, 2005.
- [12] J.R. Graef, S. Heidarkhani, L. Kong, A variational approach to a Kirchhoff-type problem involving two parameters, Results Math. 63 (2013), 877–889.
- [13] J.R. Graef, S. Heidarkhani, L. Kong, Variational-hemivariational inequalities of Kirchhoff-type with small perturbations of nonhomogeneous Neumann boundary conditions, Math. Eng. Sci. Aero. 8 (2017), 345–357.
- [14] J.R. Graef, S. Heidarkhani, L. Kong, S. Moradi, On an anisotropic discrete boundary value problem of Kirchhoff type, J. Difference Equ. Appl. 27 (2021), 1103–1119.
- [15] J.R. Graef, S. Heidarkhani, L. Kong, A. Ghobadi, Existence of multiple solutions to a P-Kirchhoff problem, Differ. Equ. Appl. 14 (2022), 227–237.
- [16] L. Guo, Y. Sun, G. Shi, Ground states for fractional nonlocal equations with logarithmic nonlinearity, Opuscula Math. 42 (2022), 157–178.
- [17] D.D. Hai, Positive radial solutions for singular quasilinear elliptic equations in a ball, Publ. Res. Inst. Math. Sci. 50 (2014), 341–362.
- [18] W. He, D. Qin, Q. Wu, Existence, multiplicity and nonexistence results for Kirchhoff type equations, Adv. Nonlinear Anal. 10 (2021), 616–635.
- [19] G. Kirchhoff, Mechanik, Teubner, Leipzig, 1883.
- [20] Q. Morris, R. Shivaji, I. Sim, Existence of positive radial solutions for a superlinear semipositone p-Laplacian problem on the exterior of a ball, Proc. Roy. Soc. Edinburgh Sect. A 148 (2018), 409–428.
- [21] H. Pi, Y. Zeng, Existence results for the Kirchhoff type equation with a general nonlinear term, Acta Math. Scientia 42 (2022), 2063–2077.
- [22] D. Qin, V.D. Radulescu, X. Tang, Ground states and geometrically distinct solutions for periodic Choquard–Pekar equations, J. Differential Equations 275 (2021), 652–683.
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- [24] L. Wang, K. Xie, B. Zhang, Existence and multiplicity of solutions for critical Kirchhoff-type p-Laplacian problems, J. Math. Anal. Appl. 458 (2018), 361–378.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
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