The nodal solutions of equations are considered to be more difficult than the positive solutions and the ground state solutions. Based on this, this paper intends to study nodal solutions for a kind of Schr<span st...The nodal solutions of equations are considered to be more difficult than the positive solutions and the ground state solutions. Based on this, this paper intends to study nodal solutions for a kind of Schr<span style="white-space:nowrap;">ö</span>dinger-Poisson equation. We consider a class of Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger-Poisson equation with variable potential under weaker conditions in this paper. By introducing some new techniques and using truncated functional, Hardy inequality and Poho<span style="white-space:nowrap;"><span style="white-space:nowrap;">ž</span></span>aev identity, we obtain an existence result of a least energy sign-changing solution and a ground state solution for this kind of Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger-Poisson equation. Moreover, the energy of the sign-changing solution is strictly greater than the ground state energy.展开更多
This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We stud...This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.展开更多
文摘The nodal solutions of equations are considered to be more difficult than the positive solutions and the ground state solutions. Based on this, this paper intends to study nodal solutions for a kind of Schr<span style="white-space:nowrap;">ö</span>dinger-Poisson equation. We consider a class of Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger-Poisson equation with variable potential under weaker conditions in this paper. By introducing some new techniques and using truncated functional, Hardy inequality and Poho<span style="white-space:nowrap;"><span style="white-space:nowrap;">ž</span></span>aev identity, we obtain an existence result of a least energy sign-changing solution and a ground state solution for this kind of Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger-Poisson equation. Moreover, the energy of the sign-changing solution is strictly greater than the ground state energy.
文摘This paper mainly discusses the following equation: where the potential function V : R<sup>3</sup> → R, α ∈ (0,3), λ > 0 is a parameter and I<sub>α</sub> is the Riesz potential. We study a class of Schrödinger-Poisson system with convolution term for upper critical exponent. By using some new tricks and Nehair-Pohožave manifold which is presented to overcome the difficulties due to the presence of upper critical exponential convolution term, we prove that the above problem admits a ground state solution.
