In this paper, it is proved that the following boundary value problem [GRAPHICS] admits infinitely many solution for 0 < lambda < lambda-1, n greater-than-or-equal-to 5 and for ball regions OMEGA = B(R)(0).
We show for the Benjamin-Ono equation an existence uniqeness theorem in Sobolev spaces of arbitrary fractional order s greater-than-or-equal-to 2, provided the initial data is given in the same space.
In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
This paper concerns the following nonlinear elliptic equation:{?u + K(y)u^((N+2)/(N-2)±ε)= 0, u > 0, y ∈ R^N,u ∈ D^(1,2)(R^N),where ε > 0, N≥5, K(y) is positive and radially symmetric. We show that, un...This paper concerns the following nonlinear elliptic equation:{?u + K(y)u^((N+2)/(N-2)±ε)= 0, u > 0, y ∈ R^N,u ∈ D^(1,2)(R^N),where ε > 0, N≥5, K(y) is positive and radially symmetric. We show that, under some local conditions on K(y), this problem has large number of bubble solutions if ε is small enough. Moreover, for each m ∈ [2, N- 2),there exists solutions whose functional energy is in the order of ε^(-(N-2-m)/((N-2)~2)).展开更多
In this paper,the authors provide a brief introduction of the path-dependent partial differential equations(PDEs for short)in the space of continuous paths,where the path derivatives are in the Dupire(rather than Fr&#...In this paper,the authors provide a brief introduction of the path-dependent partial differential equations(PDEs for short)in the space of continuous paths,where the path derivatives are in the Dupire(rather than Fréchet)sense.They present the connections between Wiener expectation,backward stochastic differential equations(BSDEs for short)and path-dependent PDEs.They also consider the well-posedness of path-dependent PDEs,including classical solutions,Sobolev solutions and viscosity solutions.展开更多
文摘In this paper, it is proved that the following boundary value problem [GRAPHICS] admits infinitely many solution for 0 < lambda < lambda-1, n greater-than-or-equal-to 5 and for ball regions OMEGA = B(R)(0).
文摘We show for the Benjamin-Ono equation an existence uniqeness theorem in Sobolev spaces of arbitrary fractional order s greater-than-or-equal-to 2, provided the initial data is given in the same space.
文摘In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
基金Tian Yuan Special Funds of National Natural Science Foundation of China (Grant No. 11426088)
文摘This paper concerns the following nonlinear elliptic equation:{?u + K(y)u^((N+2)/(N-2)±ε)= 0, u > 0, y ∈ R^N,u ∈ D^(1,2)(R^N),where ε > 0, N≥5, K(y) is positive and radially symmetric. We show that, under some local conditions on K(y), this problem has large number of bubble solutions if ε is small enough. Moreover, for each m ∈ [2, N- 2),there exists solutions whose functional energy is in the order of ε^(-(N-2-m)/((N-2)~2)).
基金supported by the National Key R&D Program of China(Nos.2018YFA0703900,2020YFA0712700,2018YFA0703901)the National Natural Science Foundation of China(Nos.12031009,12171280)the Natural Science Foundation of Shandong Province(Nos.ZR2021YQ01,ZR2022JQ01).
文摘In this paper,the authors provide a brief introduction of the path-dependent partial differential equations(PDEs for short)in the space of continuous paths,where the path derivatives are in the Dupire(rather than Fréchet)sense.They present the connections between Wiener expectation,backward stochastic differential equations(BSDEs for short)and path-dependent PDEs.They also consider the well-posedness of path-dependent PDEs,including classical solutions,Sobolev solutions and viscosity solutions.
