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
The Nanwenghe Wetlands Reserve in the Yile'huli Mountains is a representative region of the Xing'an permafrost.The response of permafrost to climate change remains unclear due to limited field investigations.T...The Nanwenghe Wetlands Reserve in the Yile'huli Mountains is a representative region of the Xing'an permafrost.The response of permafrost to climate change remains unclear due to limited field investigations.Thus,longer-term responses of the ground thermal state to climate change since 2011 have been monitored at four sites with varied surface characteristics:Carex tato wetland(P1)and shrub-C.tato wetland(P2)with a multi-year average temperatures at the depth of zero annual amplitude(T_(ZAA))of−0.52 and−1.19℃,respectively;Betula platyphylla-Larix gmelinii(Rupr.)Kuzen mixed forest(P3)with T_(ZAA) of 0.17℃,and;the forest of L.gmelinii(Rupr.)Kuzen(P4)with T_(ZAA) of 1.65℃.Continuous observations demonstrate that the ecosystem-protected Xing'an permafrost experienced a cooling under a warming climate.The temperature at the top of permafrost(TTOP)rose(1.8℃ per decade)but the TZAA declined(−0.14℃ per decade),while the active layer thickness(ALT)thinned from 0.9 m in 2012 to 0.8 m in 2014 at P1.Both the TTOP and TZAA increased(0.89 and 0.06℃ per decade,respectively),but the ALT thinned from 1.4 m in 2012 to 0.7 m in 2016 at P2.Vertically detached permafrost at P3 disappeared in summer 2012,with warming rates of+0.42 and+0.17℃ per decade for TTOP and T_(ZAA),respectively.However,up to date,the ground thermal state has remained stable at P4.We conclude that the thermal offset is crucial for the preservation and persistence of the Xing'an permafrost at the southern fringe.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.
基金This study is financially supported by the program of National Natural Science Foundation of China(41401081,41871052,41771074)Joint Key Program of NSFC‒Heilongjiang Province for Regional Development(U20A2082)the Research Project of the State Key Laboratory of Frozen Soil Engineering(SKLFSE-ZT-41,SKLFSE-ZY-20).
文摘The Nanwenghe Wetlands Reserve in the Yile'huli Mountains is a representative region of the Xing'an permafrost.The response of permafrost to climate change remains unclear due to limited field investigations.Thus,longer-term responses of the ground thermal state to climate change since 2011 have been monitored at four sites with varied surface characteristics:Carex tato wetland(P1)and shrub-C.tato wetland(P2)with a multi-year average temperatures at the depth of zero annual amplitude(T_(ZAA))of−0.52 and−1.19℃,respectively;Betula platyphylla-Larix gmelinii(Rupr.)Kuzen mixed forest(P3)with T_(ZAA) of 0.17℃,and;the forest of L.gmelinii(Rupr.)Kuzen(P4)with T_(ZAA) of 1.65℃.Continuous observations demonstrate that the ecosystem-protected Xing'an permafrost experienced a cooling under a warming climate.The temperature at the top of permafrost(TTOP)rose(1.8℃ per decade)but the TZAA declined(−0.14℃ per decade),while the active layer thickness(ALT)thinned from 0.9 m in 2012 to 0.8 m in 2014 at P1.Both the TTOP and TZAA increased(0.89 and 0.06℃ per decade,respectively),but the ALT thinned from 1.4 m in 2012 to 0.7 m in 2016 at P2.Vertically detached permafrost at P3 disappeared in summer 2012,with warming rates of+0.42 and+0.17℃ per decade for TTOP and T_(ZAA),respectively.However,up to date,the ground thermal state has remained stable at P4.We conclude that the thermal offset is crucial for the preservation and persistence of the Xing'an permafrost at the southern fringe.
