The following fractional Klein-Gordon-Maxwell system is studied<br /> <p> <img src="Edit_d0190fe4-48ad-4118-8c6c-c585ba971681.bmp" alt="" /> <br /> (-Δ)<sup><em>...The following fractional Klein-Gordon-Maxwell system is studied<br /> <p> <img src="Edit_d0190fe4-48ad-4118-8c6c-c585ba971681.bmp" alt="" /> <br /> (-Δ)<sup><em>p</em></sup> stands for the fractional Laplacian, <em>ω</em> > 0 is a constant, <em>V</em> is vanishing potential and <em>K</em> is a smooth function. Under some suitable conditions on <em>K</em> and <em>f</em>, we obtain a Palais-Smale sequence by using a weaker Ambrosetti-Rabinowitz condition and prove the ground state solution for this system by employing variational methods. In particular, this kind of problem is a vast range of applications and challenges. </p>展开更多
We study the following quasilinear Schrodinger equation-△u+V(x)u-△(u^(2))u=K(x)g(u),x∈R^(3),where the nonlinearity g(u)is asymptotically cubic at infinity,the potential V(x)may vanish at infinity.Under appropriate ...We study the following quasilinear Schrodinger equation-△u+V(x)u-△(u^(2))u=K(x)g(u),x∈R^(3),where the nonlinearity g(u)is asymptotically cubic at infinity,the potential V(x)may vanish at infinity.Under appropriate assumptions on K(x),we establish the existence of a nontrivial solution by using the mountain pass theorem.展开更多
We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential crit...We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential critical growth.The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.展开更多
In this paper,we study the existence of positive solution for the p-Laplacian equations with frac-tional critical nonlinearity{-Δ)_(p)^(s)u+V(x)|u|^(p-2)u=K(x)f(u)+P(x)|u|p_(s)^(*)-^(2)u,x∈R^(N),u∈Ds,p(RN),where s...In this paper,we study the existence of positive solution for the p-Laplacian equations with frac-tional critical nonlinearity{-Δ)_(p)^(s)u+V(x)|u|^(p-2)u=K(x)f(u)+P(x)|u|p_(s)^(*)-^(2)u,x∈R^(N),u∈Ds,p(RN),where s∈(0,1),p_(s)^(*)=Np/N-sp,N>sp,p>1 and V(x),K(x)are positive continuous functions which vanish at infinity,f is a function with a subcritical growth,and P(x)is bounded,nonnegative continuous function.By using variational method in the weighted spaces,we prove the above problem has at least one positive solution.展开更多
文摘The following fractional Klein-Gordon-Maxwell system is studied<br /> <p> <img src="Edit_d0190fe4-48ad-4118-8c6c-c585ba971681.bmp" alt="" /> <br /> (-Δ)<sup><em>p</em></sup> stands for the fractional Laplacian, <em>ω</em> > 0 is a constant, <em>V</em> is vanishing potential and <em>K</em> is a smooth function. Under some suitable conditions on <em>K</em> and <em>f</em>, we obtain a Palais-Smale sequence by using a weaker Ambrosetti-Rabinowitz condition and prove the ground state solution for this system by employing variational methods. In particular, this kind of problem is a vast range of applications and challenges. </p>
基金the National Natural Science Foundation of China(No.11901499 and No.11901500)Nanhu Scholar Program for Young Scholars of XYNU(No.201912)。
文摘We study the following quasilinear Schrodinger equation-△u+V(x)u-△(u^(2))u=K(x)g(u),x∈R^(3),where the nonlinearity g(u)is asymptotically cubic at infinity,the potential V(x)may vanish at infinity.Under appropriate assumptions on K(x),we establish the existence of a nontrivial solution by using the mountain pass theorem.
基金Natural Science Foundation of China(Grant Nos.11601190 and 11661006)Natural Science Foundation of Jiangsu Province(Grant No.BK20160483)Jiangsu University Foundation Grant(Grant No.16JDG043)。
文摘We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential critical growth.The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.
基金supported by the National Natural Science Foundation of China(Nos.12171497,11771468,11971027)。
文摘In this paper,we study the existence of positive solution for the p-Laplacian equations with frac-tional critical nonlinearity{-Δ)_(p)^(s)u+V(x)|u|^(p-2)u=K(x)f(u)+P(x)|u|p_(s)^(*)-^(2)u,x∈R^(N),u∈Ds,p(RN),where s∈(0,1),p_(s)^(*)=Np/N-sp,N>sp,p>1 and V(x),K(x)are positive continuous functions which vanish at infinity,f is a function with a subcritical growth,and P(x)is bounded,nonnegative continuous function.By using variational method in the weighted spaces,we prove the above problem has at least one positive solution.
