PDF(424 KB)
PDF(424 KB)
PDF(424 KB)
一类带变号权函数的p-Kirchhoff方程正解的存在性与多解性
Multiplicity of Positive Solutions to a p-Kirchhoff Equation with Sign-Changing Weight Functions
利用变分方法, 通过对Nehari流形进行分解,证明了一类带变号权函数的p-Kirchhoff方程正解的存在性与多解性.
We study the multiplicity of positive solutions to a p-Kirchhoff equation with sign-changing weight functions. These positive solutions are obtained by the variational methods and the decomposition of the Nehari manifold.
p-Kirchhoff方程 / 变号权函数 / Nehari流形 / 正解 {{custom_keyword}} /
p-Kirchhoff equation / sign-changing weight functions / Nehari manifold / positive solution {{custom_keyword}} /
[1] Alves C. O., Figueiredo G. M., Nonlinear perturbations of a periodic Kirchhoff equation in RN, Nonlinear Anal., 2012, 75(5): 2750-2759.
[2] Ambrosetti A., Brezis H., Cerami G., Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal., 1994, 122(2): 519-543.
[3] Brown K. J., Zhang Y. P., The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function, J. Differential Equations, 2003, 193(2): 481-499.
[4] Chen C. S., Huang J. C., Liu L. H., Multiple solutions to the nonhomogeneous p-Kirchhoff elliptic equation with concave-convex nonlinearities, Appl. Math. Lett., 2013, 26(7): 754-759.
[5] Chen C. Y., Kuo Y. C., Wu T. F., The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions, J. Differential Equations, 2011, 250(4): 1876-1908.
[6] Corrêa F. J. S. A., On positive solutions of nonlocal and nonvariational elliptic problems, Nonlinear Anal., 2004, 59(7): 1147-1155.
[7] Dreher M., The Kirchhoff equation for the p-Laplacian, Rend Semin Mat Univ Politec Torino., 2006, 64(2): 217-238.
[8] Dreher M., The wave equation for the p-Laplacian, Hokkaido Math J., 2007, 36(1): 21-52.
[9] Huang J. C., Chen C. S., Xiu Z. H., Existence and multiplicity results for a p-Kirchhoff equation with a concave-convex term, Appl. Math. Lett., 26(11): 1070-1075.
[10] Kirchhoff G., Vorlesungen über Mathematishe Physik, BG Teubner, 1876.
[11] Li Y. H., Li F. Y., Shi J. P., Existence of a positive solution to Kirchhoff type problems without compactness conditions, J. Differential Equations, 2012, 253(7): 2285-2294.
[12] Lucio D., Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results, Ann Inst H. Poincaré Anal Non Linéaire., 1998, 15(4): 493-516.
[13] Ma T. F., Muñoz Rivera J. E., Positive solutions for a nonlinear nonlocal elliptic transmission problem, Appl. Math. Lett., 2003, 16(2): 243-248.
[14] Mao A. M., Luan S. X., Sign-changing solutions of a class of nonlocal quasilinear elliptic boundary value problems, J. Math. Anal. Appl., 2011, 383(1): 239-243.
[15] Mao A. M., Zhang Z. T., Sign-changing and multiple solutions of Kirchhoff type problems without the P. S. condition, Nonlinear Anal., 2009, 70(3): 1275-1287.
[16] Miotto M. L., Miyagaki O. H., Multiple positive solutions for semilinear Dirichlet problems with sign-changing weight function in infinite strip domains, Nonlinear Anal., 2009, 71(7-8): 3434-3447.
[17] Sun J. J., Tang C. L., Existence and multiplicity of solutions for Kirchhoff type equations, Nonlinear Anal., 2011, 74(4): 1212-1222.
[18] Wu T. F., On semilinear elliptic equations involving concave-convex nonlinearities and sign-changing weight function, J. Math. Anal. Appl., 2006, 318(1): 253-270.
国家自然科学基金资助项目(11071149, 11301313)
/
| 〈 |
|
〉 |
