AbstractIn this note, we consider the polyharmonic system (−Δ)mu=vα, (−Δ)mv=uβ in RN with N>2m and α⩾1, β⩾1, where (−Δ)m is the polyharmonic operator. For 1/(α+1)+1/(β+1)>(N−2m)/N, we prove the non-existence of non-negative, radial, smooth solutions. For 1<α,β<(N+2m)/(N−2m), we show the non-existence of non-negative smooth solutions. In addition, for either (N−2m)β<Nα+2m or (N−2m)α<Nβ+2m with α,β>1, we show the non-existence of non-negative smooth solutions for polyharmonic system of inequalities (−Δ)mu⩾vα, (−Δ)mv⩾uβ. More general, we can prove that all the above results hold for the system (−Δ)mu=vα,(−Δ)nv=uβ in RN with N>max{2m,2n} and α⩾1, β⩾1
AbstractIn this paper we study the existence of positive solutions for the system of generalized Lid...
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AbstractFor p≥0, let σ=n+2−p(n−2). Let K(x) be nonnegative in Rn and satisfy the conditions that |x|...
AbstractWe study the existence of positive solutions of the m-polyharmonic nonlinear elliptic equati...
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This work deals with the system (−Δ)mu = a(x) vp, (−Δ)mv = b(x) uq with Dirichlet boundary condition...
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AbstractIn this paper we study the existence of positive solutions for the system of generalized Lid...
AbstractIn this paper, by the method of moving planes, we establish the monotonicity and symmetry fo...
AbstractIn this paper we are concerned with the existence and concentration of positive solutions fo...
AbstractFor p≥0, let σ=n+2−p(n−2). Let K(x) be nonnegative in Rn and satisfy the conditions that |x|...
AbstractWe study the existence of positive solutions of the m-polyharmonic nonlinear elliptic equati...
AbstractIn this paper we give an existence and uniqueness theorem for a nonlinear second order homog...
AbstractWe study the existence of solutions for the nonlinear elliptic system {−Mλ,Λ+(D2u)=f1(x,u)+h...
AbstractThis paper deals with the existence of positive solutions to a Dirichlet problem for the sup...
This work deals with the system (−Δ)mu = a(x) vp, (−Δ)mv = b(x) uq with Dirichlet boundary condition...
AbstractWe investigate the existence, nonexistence, and multiplicity of positive radial solutions fo...
AbstractIn this paper we study the existence of positive large solutions for the equation Δpu+λ|∇u|p...
AbstractWe will show that the problem−Δu=|u|4/(N−2)uin Ω,u=0on ∂Ω has at least two pairs of solution...
AbstractIn this paper, we study the existence of multiple positive solutions to some Hamiltonian ell...
AbstractIn this note, we consider the quasilinear elliptic equation ±Δpu=h(x)um+H(x)un in RN (N⩾3), ...
AbstractIn this paper, we study the asymptotic behaviour as p→∞ of the radial solution of the proble...
AbstractIn this paper we study the existence of positive solutions for the system of generalized Lid...
AbstractIn this paper, by the method of moving planes, we establish the monotonicity and symmetry fo...
AbstractIn this paper we are concerned with the existence and concentration of positive solutions fo...