Access the full text.
Sign up today, get DeepDyve free for 14 days.
(2001)
On existence of solutions for a class of problem involving a nonlinear operator
M. Chipot, J.F. Rodrigues (1992)
On a class of nonlocal nonlinear elliptic problemsRAIRO Modél. Math. Anal. Numér., 26
Zhitao Zhang, K. Perera (2006)
Sign changing solutions of Kirchhoff type problems via invariant sets of descent flowJournal of Mathematical Analysis and Applications, 317
C.F. Vasconcellos (1992)
On a nonlinear stationary problem in unbounded domainsRev. Mat. Univ. Complut. Madrid, 5
(1997)
An operator equation suggested by a class of nonlinear stationary problems
Tai-Chia Lin, Juncheng Wei (2006)
Spikes in Two-component Systems of Nonlinear Schrodinger Equations with Trapping PotentialsJournal of Differential Equations, 229
E.N. Dancer, J. Wei, T. Weth (2010)
A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger systemAnn. Inst. H. Poincaré Anal. Non Linéaire, 27
Tai-Chia Lin, Juncheng Wei (2005)
Ground State of N Coupled Nonlinear Schrödinger Equations in Rn,n≤3Communications in Mathematical Physics, 255
E. Dancer, Juncheng Wei, T. Weth (2010)
A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger systemAnnales De L Institut Henri Poincare-analyse Non Lineaire, 27
A. Ambrosetti, P. Rabinowitz (1973)
Dual variational methods in critical point theory and applicationsJournal of Functional Analysis, 14
D. Figueiredo, Orlando Lopes (2008)
Solitary waves for some nonlinear Schrödinger systems, 25
J. Lions (1978)
On Some Questions in Boundary Value Problems of Mathematical PhysicsNorth-holland Mathematics Studies, 30
E. Dancer, Juncheng Wei (2008)
Spike solutions in coupled nonlinear Schrödinger equations with attractive interactionTransactions of the American Mathematical Society, 361
M. Chipot, B. Lovat (1997)
Some remarks on non local elliptic and parabolic problemsNonlinear Analysis-theory Methods & Applications, 30
K. Fan (1953)
Minimax Theorems.Proceedings of the National Academy of Sciences of the United States of America, 39 1
T. Ma, J. Rivera (2003)
Positive solutions for a nonlinear nonlocal elliptic transmission problemAppl. Math. Lett., 16
A. Ambrosetti, E. Colorado (2007)
Standing waves of some coupled nonlinear Schrödinger equationsJournal of the London Mathematical Society, 75
C. Alves, F. Corrêa, G. Figueiredo (2010)
ON A CLASS OF NONLOCAL ELLIPTIC PROBLEMS WITH CRITICAL GROWTHDifferential Equations and Applications
C.O. Alves, F.J. Correa (2001)
S.AOn existence of solutions for a class of problem involving a nonlinear operator. Comm. Appl. Nonlinear Anal., 8
M. Sadiku (2018)
Variational MethodsComputational Electromagnetics with MATLAB®
M. Chipot, J. Rodrigues (1992)
On a class of nonlocal nonlinear elliptic problemsMathematical Modelling and Numerical Analysis, 26
Anmin Mao, Zhitao Zhang (2009)
Sign-changing and multiple solutions of Kirchhoff type problems without the P.S. conditionNonlinear Analysis-theory Methods & Applications, 70
G. Anello (2011)
A uniqueness result for a nonlocal equation of Kirchhoff type and some related open problemJournal of Mathematical Analysis and Applications, 373
C. Alves, F. Corrêa, T. Ma (2005)
Positive solutions for a quasilinear elliptic equation of Kirchhoff typeComputers & Mathematics With Applications, 49
C. Vasconcelos (1992)
On a Nonlinear Stationary Problem in Unbound Domains.Revista Matematica Complutense, 5
M. Chipot, B. Lovat (1997)
Proceedings of the Second World Congress of Nonlinear Analysts, Part 7 (Athens, 1996)
Juncheng Wei, T. Weth (2008)
Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger EquationsArchive for Rational Mechanics and Analysis, 190
E. Fadell, P. Rabinowitz (1977)
Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systemsInventiones mathematicae, 45
G. Kirchhoff (1883)
Mechanik
T. Bartsch, Zhi-Qiang Wang, Juncheng Wei (2007)
Bound states for a coupled Schrödinger systemJournal of Fixed Point Theory and Applications, 2
K. Perera, Zhitao Zhang (2006)
Nontrivial solutions of Kirchhoff-type problems via the Yang indexJournal of Differential Equations, 221
K. Perera, R. Agarwal, D. O’Regan (2010)
Morse Theoretic Aspects of $p$-Laplacian Type Operators
B. Sirakov (2010)
Least Energy Solitary Waves for a System of Nonlinear Schr¨odinger Equations in R n
B. Ricceri (2008)
On an elliptic Kirchhoff-type problem depending on two parametersJournal of Global Optimization, 46
J.L. Lions (1978)
Contemporary developments in continuum mechanics and partial differential equations, Vol.30 of North-Holland Math. Stud., North-Holland, Amsterdam
Firstly, we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type. Then a multiplicity result is established by cohomological index of Fadell and Rabinowitz. We also consider the critical case and prove existence of positive least energy solution when the parameter β is sufficiently large.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Apr 5, 2016
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.