Ir al contenido

Documat

Multiple Positive Solutions for Kirchhoff-Type Problems Involving Supercritical and Critical Terms

  • Deke Wu [2] ; Hongmin Suo [1] ; Jun Lei [1]
    1. [1] Guizhou Minzu University

      Guizhou Minzu University

      China

    2. [2] Guiyang Institute of Information Science and Technology
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 3, 2024
  • Idioma: inglés
  • DOI: 10.1007/s12346-024-00999-w
  • Enlaces
  • Resumen

    • We investigate the multiplicity results of positive solutions for a Kirchhoff-type problems with supercritical and critical nonlinear terms in a ball. By employing the Nehari method and Lusternik–Schnirelmann category theory to an auxiliary problems, we note that there is a relationship between the number of maxima in the coefficient function of the critical term and the number of positive solutions for the problems.

  • Referencias bibliográficas
    • 1. Kirchhoff, G.: Mechanik [M]. Teubner, Leipzig, Germany (1883)
    • 2. Lions, J.L.: On some questions in boundary value problems of mathematical physics. North-Holland Math. Stud. 30, 284–346 (1978)
    • 3. Alves, C.O., Correa, F.J.S.A., Ma, T.F.: Positive solutions for a quasilinear elliptic equation of Kirchhoff type. Comput. Math. Appl....
    • 4. Zhang, Z., Perera, K.: Sign-changing solutions of Kirchhoff type problems via invariant sets of descent flow. J. Math. Anal. Appl. 317,...
    • 5. Jin, J., Wu, X.: Infinitely many radial solutions for Kirchhoff–type problems in R3. J. Math. Anal. Appl. 369, 564–574 (2010)
    • 6. Li, Y., Li, F., Shi, J.: Existence of positive solutions to Kirchhoff type problems with zero mass. J. Math. Anal. Appl. 410, 361–374 (2014)
    • 7. Fan, H.: Multiple positive solutions for a class of Kirchhoff type problems involving critical Sobolev exponents. J. Math. Anal. Appl....
    • 8. Lei, C.Y., Liao, J.F., Tang, C.L.: Multiple positive solutions for Kirchhoff type of problem with singularity and critical exponents. J....
    • 9. Wang, Y.: The third solution for a Kirchhofftype problem with a critical exponent. J. Math. Anal. Appl. 526(1), 127174 (2023)
    • 10. Fan, H.N.: Positive solutions for a Kirchhoff–type problem involving multiple competitive potentials and critical Sobolev exponent. Nonlinear...
    • 11. Qian, X.T.: Existence and concentration of ground state solutions for a class of nonlocal problem in RN . Nonlinear Anal. 203, 112170...
    • 12. Qian, X.T.: Multiplicity of positive solutions for a class of nonlocal problem involving critical exponent. Electron. J. Qual. Theory...
    • 13. Lei, C.Y., Liu, G.S.: Near resonance for a Kirchhoff–Schrödinger–Newton system. Indian. J. Pure. Appl. Math. 52, 363–368 (2021)
    • 14. Lei, J., Suo, H.M.: Multiple solutions of Kirchhoff type equations involving Neumann conditions and critical growth. AIMS Math. 6, 3821–3837...
    • 15. Wang, Y., Wei, W., Zhou, Y.: The existence, uniqueness, and multiplicity of solutions for two fractional nonlocal equations. Axioms 12,...
    • 16. Che, G., Chen, H.: Existence and multiplicity of positive solutions for Kirchhoff–Schrödinger–Poisson system with critical growth. Rev....
    • 17. Qian, X., Chao, W.: Existence of positive solutions for nonlocal problems with indefinite nonlinearity. Bound. Value. Probl. 2020, 1–13...
    • 18. Wu, D., Suo, H., Peng, L.Y., et al.: Existence and multiplicity of positive solutions for a class of Kirchhoff type problems with singularity...
    • 19. Lei, C.Y., Chu, C.M., Suo, H.M.: Positive solutions for a nonlocal problem with singularity. Electron. J. Differ. Equ. 85, 1–9 (2017)
    • 20. Wang, Y., Suo, H.M., Lei, C.Y.: Multiple positive solutions for a nonlocal problem involving critical exponent. Electron. J. Differ. Equ....
    • 21. Lei, C.Y., Liao, J.F., Suo, H.M.: Multiple positive solutions for a class of nonlocal problems involving a sign-changing potential. Electron....
    • 22. Lei, C.Y., Liao, J.F.: Positive solutions for a Kirchhoff–type equation with critical and supercritical nonlinear terms. Bull. Malays....
    • 23. Heidarkhani, S., Kou, K.I., Salari, A.: Three weak solutions for a degenerate nonlocal singular sublinear problem. Differ. Equ. Appl....
    • 24. Caristi, G., Heidarkhani, S., Salari, A., Tersian, S.A.: Multiple solutions for degenerate nonlocal problems. Appl. Math. Lett. 84, 26–33...
    • 25. Chu, J., Heidarkhani, S., Kou, K.I., Salari, A.: Weak solutions and energy estimates for a degenerate nonlocal problem involving sub-linear...
    • 26. Heidarkhani, S., Henderson, J.: Multiple solutions for a nonlocal perturbed elliptic problem of pKirchhoff type. Comm. Appl. Nonlinear...
    • 27. Kefi, K., Saoudi, K., Al-Shomrani, M.M.: A Kirchhoff–Biharmonic problem involving singular nonlinearities and Navier boundary conditions....
    • 28. Graef, J.R., Heidarkhani, S., Kong, L.: A variational approach to a Kirchhoff-type problem involving a parameter. Results Math. 63, 877–889...
    • 29. Figueiredo, G.M.: Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument. J. Math....
    • 30. Figueiredo, G.M., Ikoma, N., Santos Jior, J.R.: Existence and concentration result for the Kirchhoff type equations with general nonlinearities....
    • 31. Lu, L.: Signed and sign-changing solutions for a Kirchhoff-type equation in bounded domains. J. Math. Anal. Appl. 432, 965–982 (2015)
    • 32. Wang, L., Xie, K., Zhang, B.L.: Existence and multiplicity of solutions for critical Kirchhoff-type p-Laplacian problems. J. Math. Anal....
    • 33. Lei, J., Suo, H.M.: Multiple positive solutions for a Schrödinger-Poisson system with critical and supercritical growths. Izvestiya Mathematics...
    • 34. Do Marcos, J., Rul, B., Ubilla, P.: On supercritical Sobolev type inequalities and related elliptic equations. Calc. Var. Partial Differ....
    • 35. Struwe, M.: Variational Methods, 2nd edn. Springer-Verlag, Berlin, Heidelberg (1996)
    • 36. Han, P.G.: Multiple solutions to singular critical elliptic equations. Isr. J. Math. 156, 359–380 (2006)
    • 37. Cao, D.M., Chabrowski, J.: Multiple solutions of nonhomogeneous elliptic equation with critical nonlinearity. Differ. Integral Equ. 10,...
    • 38. Liao, J.F., Liu, J., Zhang, P., Tang, C.L.: Existence and multiplicity of positive solutions for a class of elliptic equations involving...
    • 39. Zhu, M.: Uniqueness results through a Priori estimates I. A three dimensional Neumann problem. J. Differ. Equ. 154, 284–317 (1999)
    • 40. Lions, P.L.: The concentration-compactness principle in the calculus of variations. The limit case I. Rev. Mat. Iberoam. 1, 145–201 (1985)
    • 41. Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 48, 324–353 (1974)
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno