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Abstract: We consider the following convective Neumann systems: $\begin{equation*}\left(\mathrm{S}\right)\qquad\left\{\begin{array}{ll}-\Delta_{p_1}u_1+\frac{|\nabla u_1|^{p_1}}{u_1+\delta_1}=f_1(x,u_1,u_2,\nabla u_1,\nabla u_2) \text{in}\;\Omega,\\ -\Delta _{p_2}u_2+\frac{|\nabla u_2|^{p_2}}{u_2+\delta_2}=f_2(x,u_1,u_2,\nabla u_1,\nabla u_2) \text{in}\;\Omega, \\ |\nabla u_1|^{p_1-2}\frac{\partial u_1}{\partial \eta }=0=|\nabla u_2|^{p_2-2}\frac{\partial u_2}{\partial \eta} \text{on}\;\partial\,\Omega,\end{array}\right.\end{equation*}$ where $\Omega$ is a bounded domain in $\mathbb{R}^{N}$ ($N\geq 2$) with a smooth boundary $\partial\,\Omega, \delta_1, \delta_2 > 0$ are small parameters, $\eta$ is the outward unit vector normal to $\partial\,\Omega, f_1, f_2: \Omega \times \mathbb{R}^2 \times \mathbb{R}^{2N} \rightarrow \mathbb{R}$ are Carathéodory functions that satisfy certain growth conditions, and $\Delta _{p_i}$ ($1< p_i < N,$ for $i=1,2$) are the $p$-Laplace operators $\Delta _{p_i}u_i=\mathrm{div}(|\nabla u_i|^{p_i-2}\nabla u_i)$, for $u_i \in W^{1,p_i}(\Omega).$ In order to prove the existence of solutions to such systems, we use a sub-supersolution method. We also obtain nodal solutions by constructing appropriate sub-solution and super-solution pairs. To the best of our knowledge, such systems have not been studied yet.
Keywords: Neumann elliptic systems, gradient dependence, subsolution method, supersolution method, nodal solutions
Published in DiRROS: 16.02.2024; Views: 152; Downloads: 47
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Abstract: At the 1000km geographical distance in Dinaric montane forests of silver fir (Abies alba Mill.) and European beech (Fagus sylvatica L.), the tree response from the north-western sites towards southern, warmer and dryer sites was performed during three consecutive growing seasons (2011, 2012 and 2013). On eleven permanent plots, positioned in uneven-aged beech and fir forests above 800m along the geographical gradient, the physiological and morphological response to light intensity were measured in predefined light categories based on the analysis of hemispherical photos. Radial growth was analysed on all plots and compared to precipitation, temperature and two drought indexes. Analysis showed a decrease in the cumulative precipitation and no change in temperature between plots. Beech was most efficient in the open area light conditions, while fir proved most efficient under shelter. Physiological response for beech increased towards SE and reached its maximal values in the middle of transect, while fir%s response decreased from the NW towards SE. Tendency to plagiotropic growth decreased from NW to SE in both species. Growth response to climatic parameters is weak, stronger in fir than in beech and decreasing towards SE.
Keywords: beech, uneven aged forests, silviculture, latitudinal gradient, response, silver fir
Published in DiRROS: 13.11.2019; Views: 2080; Downloads: 1375
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Abstract: Rastline, ki uspevajo v gorah, so pogosto izpostavljene stresnim razmeram, predvsem povečani jakosti sevanja UV-B, skrajnim temperaturnim razmeram ter pomanjkanju vode in hranil. Odziv smreke na okoljske razmere je kompleksen. Pri enoletnih iglicah v visokogorju smo izmerili manjšo fotokemično učinkovitost in vsebnost klorofilov, kar kaže na občutljivost mladih iglic, kjer zaščitni mehanizmi še niso dokončno razviti. Pri starejših iglicah razlika ni bila več statistično značilna, zato sklepamo, da se poškodbe v drugem in tretjem letu preprečijo ali popravijo. Pri dveletnih iglicah smreke z visokogorskega rastišča je bil dihalni potencial značilno manjši in vsebnostUV-B absorbirajočih snovi značilno večja, kar pojasnjujemo s tem, da so dveletne iglice z visokogorskega rastišča med tremi starostnimi razredi najbolj odporne proti UV-B sevanju. Iz rezultatov sicer ne moremo sklepati, v kolikšni meri je k odzivu rastline prispeval posamezni stresni dejavnik, vendar lahko trdimo, da je smreka razmeroma dobro prilagojena na velike jakosti UV-B sevanja in stresne razmere, kakršne vladajo v visokogorju.
Keywords: smreka, Picea abies, drevesa, UV-B sevanje, fotokemična učinkovitost, ETS, UV-B absorbirajoče snovi, vsebnost klorofila, višinski gradient, visokogorsko rastišče, stres
Published in DiRROS: 12.07.2017; Views: 4595; Downloads: 1842
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