A critical Kirchhoff‐type problem involving the ‐Laplacian

Mathematische Nachrichten - Tập 287 Số 2-3 - Trang 184-193 - 2014
F. Cammaroto1,2, Luca Vilasi2
1Because of a surprising coincidence of names within the same department, we have to point out that the author was born on 4 August 1968.
2Department of Mathematics and Computer Science, University of Messina, Viale F. Stagno D׳Alcontres, 31, 98166 Messina, Italy

Tóm tắt

In this paper we provide an existence result for a nonlocal problem of Kirchhoff‐type which involves both the p‐ and the q‐Laplacian and contains a critical term. Our approach is variational: we derive the existence of one non‐trivial solution via the multidimensional mountain pass theorem.

Từ khóa


Tài liệu tham khảo

Aris R., 1979, Mathematical Modelling Techniques, Res. Notes Math

Chabrowski J., 2008, Multiple solutions for a nonlinear Neumann problem involving a critical Sobolev exponent, Note Mat., 1, 15

Cherfils L., 2005, On the stationary solutions of generalized reaction diffusion equations with ‐Laplacian, Commun. Pure Appl. Anal., 4, 9, 10.3934/cpaa.2005.4.9

10.1063/1.1704233

10.1016/S0362-546X(02)00150-5

10.1007/978-3-642-93111-6

10.1016/j.na.2006.12.008

10.1016/j.na.2009.01.066

Li G., 2009, Multiple solutions for the ‐Laplacian problem with critical exponent, Acta Math. Sc., 29, 903, 10.1016/S0252-9602(09)60077-1

10.4171/RMI/6

10.1007/978-1-4757-2061-7

E. S.Medeiros Existência e concentração de solução para op‐Laplaciano com condição de Neumann(PhD Thesis UNICAMP Brazil 2001).

Rabinowitz P. H., 1986, CBMS Regional Conference Series in Mathematics

Sidiropoulos N. E., 2010, Existence of solutions to indefinite quasilinear elliptic problems of ‐Laplacian type, Electron. J. Differ. Equ., 2010, 1

10.1103/PhysRevA.36.965

10.1155/2009/185319

10.1016/j.jmaa.2011.04.090

10.1016/j.na.2011.11.035

Thông tin
Thông tin xuất bản

Mathematische Nachrichten

Tập 287 Số 2-3

184-193

Thông tin tác giả