The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition.Using variational tools together with suitable...The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition.Using variational tools together with suitable truncation and minimax techniques with Morse theory,the authors prove the existence of one and three nontrivial weak solutions,respectively.展开更多
In 1955, Serre gave an open problem on freeness of projective modules over polynomial ring over a field. In fact, it was proved by Serre in 1958 that if P is a finitely generated projective module over R[x<sub>1...In 1955, Serre gave an open problem on freeness of projective modules over polynomial ring over a field. In fact, it was proved by Serre in 1958 that if P is a finitely generated projective module over R[x<sub>1</sub>,…, x<sub>n</sub>], then P is stably isomorphic to a free module.展开更多
基金supported by the National Natural Science Foundation of China (No. 11201095)the Fundamental Research Funds for the Central Universities (No. 3072022TS2402)+1 种基金the Postdoctoral research startup foundation of Heilongjiang (No. LBH-Q14044)the Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province (No. LC201502)
文摘The aim of this paper is the study of a double phase problems involving superlinear nonlinearities with a growth that need not satisfy the Ambrosetti-Rabinowitz condition.Using variational tools together with suitable truncation and minimax techniques with Morse theory,the authors prove the existence of one and three nontrivial weak solutions,respectively.
基金Project supported by the National Natural Science Foundation of China
文摘In 1955, Serre gave an open problem on freeness of projective modules over polynomial ring over a field. In fact, it was proved by Serre in 1958 that if P is a finitely generated projective module over R[x<sub>1</sub>,…, x<sub>n</sub>], then P is stably isomorphic to a free module.
