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
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.
