This paper is concerned with the nonexistence and existence, multiplicity and bifurcation of solutions for critical semilinear polyharmonic equations. Following the ideas due to Brezis and Nirenberg[1], we obtain the ...This paper is concerned with the nonexistence and existence, multiplicity and bifurcation of solutions for critical semilinear polyharmonic equations. Following the ideas due to Brezis and Nirenberg[1], we obtain the extensions of [1] and partially confirm Pucci and Serrin[2] conjecture; by employing the abstract critical point theorem, the multiple results and bifurcation for the problem are obtained.展开更多
In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we ...In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.展开更多
This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes...This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.展开更多
In this paper we consider the existence and asymptotic estimates of global solutions and finite time blowup of local solutions of quasilinear parabolic equation with critical Sobolev exponent and with lower energy ini...In this paper we consider the existence and asymptotic estimates of global solutions and finite time blowup of local solutions of quasilinear parabolic equation with critical Sobolev exponent and with lower energy initial value; we also describe the asymptotic behavior of global solutions with high energy initial value.展开更多
In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parame...In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parameter,■ , and V : R^3→ R is a continuous potential function. For suitable assumptions on V, we show the existence of a positive ground state solution, by using the methods of the Pohozaev-Nehari manifold, Jeanjean's monotonicity trick and the concentration-compactness principle due to Lions(1984).展开更多
This paper considers the quasilinear elliptic equation where , and 0 < m < p-1 < q < +∞, Ω is a bounded domain in RN(N 3).λ is a positive number. Object is to estimate exactly the magnitute of λ* su...This paper considers the quasilinear elliptic equation where , and 0 < m < p-1 < q < +∞, Ω is a bounded domain in RN(N 3).λ is a positive number. Object is to estimate exactly the magnitute of λ* such that (1)λ has at least one positive solution if λ ∈ (0, λ*) and no positive solutions if λ > λ*. Furthermore, (1)λ has at least one positive solution when λ = λ*, and at least two positive solutions when λ ∈ (0, λ*) and . Finally, the authors obtain a multiplicity result with positive energy of (1)λ when 0 < m < p - 1 < q = (Np)/(N-p) - 1.展开更多
On a compact Riemannian manifold, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
文摘This paper is concerned with the nonexistence and existence, multiplicity and bifurcation of solutions for critical semilinear polyharmonic equations. Following the ideas due to Brezis and Nirenberg[1], we obtain the extensions of [1] and partially confirm Pucci and Serrin[2] conjecture; by employing the abstract critical point theorem, the multiple results and bifurcation for the problem are obtained.
文摘In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.
文摘This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.
基金Supported by NSF(No:10171083 and 10371021)of China Laboratory of Mathematics for Nonlinear Sciences of Fudan University
文摘In this paper we consider the existence and asymptotic estimates of global solutions and finite time blowup of local solutions of quasilinear parabolic equation with critical Sobolev exponent and with lower energy initial value; we also describe the asymptotic behavior of global solutions with high energy initial value.
基金supported by National Natural Science Foundation of China (Grant Nos. 11771468 and 11271386)supported by National Natural Science Foundation of China (Grant Nos. 11771234 and 11371212)
文摘In this paper, we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth■ where a, b > 0 are constants, μ > 0 is a parameter,■ , and V : R^3→ R is a continuous potential function. For suitable assumptions on V, we show the existence of a positive ground state solution, by using the methods of the Pohozaev-Nehari manifold, Jeanjean's monotonicity trick and the concentration-compactness principle due to Lions(1984).
文摘This paper considers the quasilinear elliptic equation where , and 0 < m < p-1 < q < +∞, Ω is a bounded domain in RN(N 3).λ is a positive number. Object is to estimate exactly the magnitute of λ* such that (1)λ has at least one positive solution if λ ∈ (0, λ*) and no positive solutions if λ > λ*. Furthermore, (1)λ has at least one positive solution when λ = λ*, and at least two positive solutions when λ ∈ (0, λ*) and . Finally, the authors obtain a multiplicity result with positive energy of (1)λ when 0 < m < p - 1 < q = (Np)/(N-p) - 1.
文摘On a compact Riemannian manifold, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
