摘要
Let r =2^d-1 ＋ 1. We investigate the diophantine inequality｜∑i=1^r λiФi（xi,yi）＋η｜〈（max 1≤i≤r{｜xi｜,｜yi｜}）^-δ,where Фi（x,y）∈X[x,y]（1≤i≤r） are nondegenerate forms of degree d = 3 or 4.
Let r =2^d-1 ＋ 1. We investigate the diophantine inequality｜∑i=1^r λiФi（xi,yi）＋η｜〈（max 1≤i≤r{｜xi｜,｜yi｜}）^-δ,where Фi（x,y）∈X[x,y]（1≤i≤r） are nondegenerate forms of degree d = 3 or 4.
基金
Acknowledgements The author was grateful to his supervisor, Professor Hongze Li, for his guidance and support. The author would like to thank Quanwu Mu for his warm heart.He gave talks on diophantine inequalities to the author individually and provided helpful discussion. This work was supported by the National Natural Science Foundation of China （Grant No. 11271249） and Specialized Research Fund for the Doctoral Program of Higher Education （No. 20120073110059）.
