Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  is concerned with the following Kirchhoff type equation #R##N##R##N#−a+b∫R3|∇u|2dx△u+V(x)u=f(x,u),x∈R3,u(x)→0,|x|→∞,#R##N##R##N#where a>0,b≥0, V∈C(R3,R)V∈C(R3,R), f∈C(R3×R,R)f∈C(R3×R,R), V(x)V(x) and f(x,u)uf(x,u)u are both allod to be sign-changing. Using a aker assumption lim|t|→∞∫0tf(x,s)ds|t|3=∞ uniformly in x∈R3x∈R3, instead of the common assumption lim|t|→∞∫0tf(x,s)ds|t|4=∞ uniformly in x∈R3x∈R3,  establish the existence of infinitely many high energy solutions of the above problem, where some new tricks are introduced to overcome the competing effect of nonlocal term. Our result unifies both asymptotically cubic or super-cubic cases, which generalizes and improves the existing ones.
['Sitong Chen', 'Xianhua Tang']
I am writing a research paper on a idea Infinitely many solutions for super-quadratic Kirchhoff-type equations with sign-changing potential ☆
[{"from": "human", "value": "I am writing a research paper on a idea Infinitely many solutions for super-quadratic Kirchhoff-type equations with sign-changing potential \u2606"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  is concerned with the following Kirchhoff type equation #R##N##R##N#\u2212a+b\u222bR3|\u2207u|2dx\u25b3u+V(x)u=f(x,u),x\u2208R3,u(x)\u21920,|x|\u2192\u221e,#R##N##R##N#where a>0,b\u22650, V\u2208C(R3,R)V\u2208C(R3,R), f\u2208C(R3\u00d7R,R)f\u2208C(R3\u00d7R,R), V(x)V(x) and f(x,u)uf(x,u)u are both allod to be sign-changing. Using a aker assumption lim|t|\u2192\u221e\u222b0tf(x,s)ds|t|3=\u221e uniformly in x\u2208R3x\u2208R3, instead of the common assumption lim|t|\u2192\u221e\u222b0tf(x,s)ds|t|4=\u221e uniformly in x\u2208R3x\u2208R3,  establish the existence of infinitely many high energy solutions of the above problem, where some new tricks are introduced to overcome the competing effect of nonlocal term. Our result unifies both asymptotically cubic or super-cubic cases, which generalizes and improves the existing ones."}]