Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.
The effects of N and P deficiency, isolated or in combination, on leaf gas exchange and fast chlorophyll (Chl) fluorescence emission were studied in common bean cv. Negrito. 10-d-old plants grown in aerated nutrient solution were supplied with high N (HN, 7.5 mol m-3) or low N (LN, 0.5 mol m-3), and also with high P (HP, 0.5 mol m-3) or low P (LP, 0.005 mol m-3). Regardless of the external P supply, in LN plants the initial fluorescence (F0) increased 12 % in parallel to a quenching of about 14 % in maximum fluorescence (Fm). As a consequence, the variable to maximum fluorescence ratio (Fv/Fm) decreased by about 7 %, and the variable to initial fluorescence ratio (Fv/F0) was lowered by 25 % in relation to control plants. In LP plants, Fv/Fm remained unchanged whilst Fv/F0 decreased slightly as a result of 5 % decline in Fm. Under N deficiency, the net photosynthetic rate (P N) halved at 6 d after imposition of treatment and so remained afterwards. As compared to LN plants, P N declined in LP plants latter and to a less extent. From 12 d of P deprivation onwards. P N fell down progressively to display rates similar to those of LN plants only at the end of the experiment. The greater P N in LP plants was not reflected in larger biomass accumulation in relation to LN beans. In general, P and N limitation affected photosynthesis parameters and growth without showing any synergistic or additive effect between deficiency of both nutrients. and J. D. Lima, P. R. Mosquim, F. M. da Matta.