In this paper, we consider the following Kirchhoff-type Schr¨odinger system −(a1 + b1 ∫R3 |∇u|2dx)△u + γV (x)u = 2α/α+β|u|α−2u|v|β in R3, −(a2 + b2 ∫R3 |∇u|2dx)△u + γV (x)u = 2β/α+β|u|α|v|β−2v in R3, u, v ∈ H1(R3), ...
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https://www.riss.kr/link?id=A103361101
Dengfeng Lu (Hubei Engineering University)
2015
English
KCI등재,SCIE,SCOPUS
학술저널
661-677(17쪽)
0
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
In this paper, we consider the following Kirchhoff-type Schr¨odinger system −(a1 + b1 ∫R3 |∇u|2dx)△u + γV (x)u = 2α/α+β|u|α−2u|v|β in R3, −(a2 + b2 ∫R3 |∇u|2dx)△u + γV (x)u = 2β/α+β|u|α|v|β−2v in R3, u, v ∈ H1(R3), ...
In this paper, we consider the following Kirchhoff-type Schr¨odinger system −(a1 + b1 ∫R3 |∇u|2dx)△u + γV (x)u = 2α/α+β|u|α−2u|v|β in R3, −(a2 + b2 ∫R3 |∇u|2dx)△u + γV (x)u = 2β/α+β|u|α|v|β−2v in R3, u, v ∈ H1(R3), where ai and bi are positive constants for i = 1, 2, γ > 0 is a parameter, V (x) and W(x) are nonnegative continuous potential functions. By applying the Nehari manifold method and the concentration-compactness principle, we obtain the existence and concentration of ground state solutions when the parameter γ is sufficiently large.
참고문헌 (Reference)
1 P. L. Lions, "The concentration-compactness principle in the calculus of variations. The locally compact case. Part I" 1 (1): 109-145, 1984
2 A. M. Mao, "Sign-changing and multiple solutions of Kirchhoff type problems without the P.S. condition" 70 (70): 1275-1287, 2009
3 C. O. Alves, "Positive solutions for a quasilinear elliptic equation of Kirchhoff type" 49 (49): 85-93, 2005
4 T. F. Ma, "Positive solutions for a nonlinear nonlocal elliptic transmission problem" 16 (16): 243-248, 2003
5 J. L. Lions, "On some questions in boundary value problems of mathematical physics, Contemporary developments in continuum mechanics and partial differential equations (Proc. Internat. Sympos., Inst. Mat., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977)" North-Holland 284-346, 1978
6 F. Cammaroto, "On a Schr¨odinger-Kirchhoff-type equation involving the p(x)-Laplacian" 81 : 42-53, 2013
7 K. Perera, "Nontrivial solutions of Kirchhoff-type problems via the Yang index" 221 (221): 246-255, 2006
8 W. Liu, "Multiplicity of high energy solutions for superlinear Kirchhoff equations" 39 (39): 473-487, 2012
9 M. F. Furtado, "Multiplicity and concentration of solutions for elliptic systems with vanishing potentials" 249 (249): 2377-2396, 2010
10 J. Wang, "Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth" 253 (253): 2314-2351, 2012
1 P. L. Lions, "The concentration-compactness principle in the calculus of variations. The locally compact case. Part I" 1 (1): 109-145, 1984
2 A. M. Mao, "Sign-changing and multiple solutions of Kirchhoff type problems without the P.S. condition" 70 (70): 1275-1287, 2009
3 C. O. Alves, "Positive solutions for a quasilinear elliptic equation of Kirchhoff type" 49 (49): 85-93, 2005
4 T. F. Ma, "Positive solutions for a nonlinear nonlocal elliptic transmission problem" 16 (16): 243-248, 2003
5 J. L. Lions, "On some questions in boundary value problems of mathematical physics, Contemporary developments in continuum mechanics and partial differential equations (Proc. Internat. Sympos., Inst. Mat., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977)" North-Holland 284-346, 1978
6 F. Cammaroto, "On a Schr¨odinger-Kirchhoff-type equation involving the p(x)-Laplacian" 81 : 42-53, 2013
7 K. Perera, "Nontrivial solutions of Kirchhoff-type problems via the Yang index" 221 (221): 246-255, 2006
8 W. Liu, "Multiplicity of high energy solutions for superlinear Kirchhoff equations" 39 (39): 473-487, 2012
9 M. F. Furtado, "Multiplicity and concentration of solutions for elliptic systems with vanishing potentials" 249 (249): 2377-2396, 2010
10 J. Wang, "Multiplicity and concentration of positive solutions for a Kirchhoff type problem with critical growth" 253 (253): 2314-2351, 2012
11 F. Cammaroto, "Multiple solutions for a Kirchhoff-type problem involving the p(x)-Laplacian operator" 74 (74): 1841-1852, 2011
12 T. Bartsch, "Multiple positive solutions for a nonlinear Schr¨odinger equation" 51 (51): 366-384, 2000
13 G. Kirchhoff, "Mechanik" Teubner 1883
14 X. M. He, "Infinitely many positive solutions for Kirchhoff-type problems" 70 (70): 1407-1414, 2009
15 F. Zhou, "High energy solutions of systems of Kirchhoff-type equations on RN" 66 (66): 1299-1305, 2013
16 X. Wu, "High energy solutions of systems of Kirchhoff-type equations in RN" 53 (53): 063508-, 2012
17 J. T. Sun, "Ground state solutions for an indefinite Kirchhoff type problem with steep potential well" 256 (256): 1771-1792, 2014
18 B. T. Cheng, "Existence results of positive solutions of Kirchhoff type problems" 71 (71): 4883-4892, 2009
19 X. Wu, "Existence of nontrivial solutions and high energy solutions for Schr¨odinger-Kirchhoff-type equations in RN" 12 (12): 1278-1287, 2011
20 X. M. He, "Existence and concentration behavior of positive solutions for a Kirchhoff equation in R3" 252 (252): 1813-1834, 2012
A NOTE ON NEVANLINNA'S FIVE VALUE THEOREM
LIE IDEALS IN TRIDIAGONAL ALGEBRA ALG∞
TWO APPLICATIONS OF LEWIS' THEOREM ON CHARACTER DEGREE GRAPHS OF SOLVABLE GROUPS
FINITE p-GROUPS WHOSE NON-CENTRAL CYCLIC SUBGROUPS HAVE CYCLIC QUOTIENT GROUPS IN THEIR CENTRALIZERS
학술지 이력
연월일 | 이력구분 | 이력상세 | 등재구분 |
---|---|---|---|
2023 | 평가예정 | 해외DB학술지평가 신청대상 (해외등재 학술지 평가) | |
2020-01-01 | 평가 | 등재학술지 유지 (해외등재 학술지 평가) | |
2010-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2008-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2006-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2004-01-01 | 평가 | 등재학술지 유지 (등재유지) | |
2001-07-01 | 평가 | 등재학술지 선정 (등재후보2차) | |
1999-01-01 | 평가 | 등재후보학술지 선정 (신규평가) |
학술지 인용정보
기준연도 | WOS-KCI 통합IF(2년) | KCIF(2년) | KCIF(3년) |
---|---|---|---|
2016 | 0.35 | 0.1 | 0.27 |
KCIF(4년) | KCIF(5년) | 중심성지수(3년) | 즉시성지수 |
0.23 | 0.2 | 0.339 | 0.04 |