This paper deals with a coupled system of fourth-order parabolic inequalities |u|t ≥ -△2^u+|v|^q, |v|t ≥-△2v+|u|p^ in S=R^n ×R^+ withp, q 〉 1, n ≥1. AFujita- Liouville type theorem is establishe...This paper deals with a coupled system of fourth-order parabolic inequalities |u|t ≥ -△2^u+|v|^q, |v|t ≥-△2v+|u|p^ in S=R^n ×R^+ withp, q 〉 1, n ≥1. AFujita- Liouville type theorem is established that the inequality system does not admit nontrivial nonnegative global solutions on S whenever n/4≤ max( p+1/pq-1, q+1/pq-1 ). Since the general maximum-comparison principle does not hold for the fourth-order problem, the authors use the test function method to get the global non-existence of nontrivial solutions.展开更多
t Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af(n) be the nth normalized Fourier coefficient of f(z). Suppose that L(sym2f, s) is the symmetric square L-functio...t Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af(n) be the nth normalized Fourier coefficient of f(z). Suppose that L(sym2f, s) is the symmetric square L-function associated with f(z), and Asym2f(n) de- notes the nth coefficient L(sym2f, s). In this paper, it is proved that where P2 (t) is a polynomial in t of degree 2. Similarly, it is obtained that where P2(t) is a polynomial in t of degree 2.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10771024,11171048)the Fundamental Research Funds for the Central Universities (No. 851011)
文摘This paper deals with a coupled system of fourth-order parabolic inequalities |u|t ≥ -△2^u+|v|^q, |v|t ≥-△2v+|u|p^ in S=R^n ×R^+ withp, q 〉 1, n ≥1. AFujita- Liouville type theorem is established that the inequality system does not admit nontrivial nonnegative global solutions on S whenever n/4≤ max( p+1/pq-1, q+1/pq-1 ). Since the general maximum-comparison principle does not hold for the fourth-order problem, the authors use the test function method to get the global non-existence of nontrivial solutions.
基金Project supported by the National Natural Science Foundation of China(Nos.10971119,11101249)the Shandong Provincial Natural Science Foundation of China(No.ZR2009AQ007)
文摘t Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af(n) be the nth normalized Fourier coefficient of f(z). Suppose that L(sym2f, s) is the symmetric square L-function associated with f(z), and Asym2f(n) de- notes the nth coefficient L(sym2f, s). In this paper, it is proved that where P2 (t) is a polynomial in t of degree 2. Similarly, it is obtained that where P2(t) is a polynomial in t of degree 2.