Positive radial solutions to a ‘semilinear’ equation involving the Pucci's operator

AbstractIn this article we prove existence of positive radially symmetric solutions for the nonlinear elliptic equationMλ,Λ+(D2u)−γu+f(u)=0inBR,u=0on∂BR,where Mλ,Λ+ denotes the Pucci's extremal operator with parameters 0<λ⩽Λ and BR is the ball of radius R in RN, N⩾3. The result applies to a wide class of nonlinear functions f, including the important model cases: (i) γ=1 and f(s)=sp, 1<p<p∗+. (ii) γ=0, f(s)=αs+sp, 1<p<p∗+ and 0⩽α<μ1+. Here p∗+ is critical exponent for Mλ,Λ+ and μ1+ is the first eigenvalue of Mλ,Λ+ in BR. Analogous results are obtained for the operator Mλ,Λ−

FACTORS INFLUENCING BEST ANNUAL RACING TIME IN FINNISH HORSES

The fixed effects of year of race, season of race, sex, method of start, annual number of starts, length of race and racetrack were evaluated on best annual racing time in Finnish Horses. Data included 1,378 records for 554 horses by 206 sires. Five models were assumed within the age groups from 3 to 6 yr. The annual number of starts, method of start and season of race effects were interrelated. An increase in number of starts was associated with considerable improvement in a horse\u27s best annual racing time. Records should not, however, be adjusted for effect of annual number of starts because it would simultaneously account for part of genetic differences among horses. The largest estimates of heritability were obtained for best annual racing time when the model included the fixed year-season and sex effects. Corresponding to this model, the estimate of repeatability for best annual racing time over the four age groups was .60 ± .03. An example of best linear unbiased predictions of sires\u27 breeding values based on progeny records in one or several ages is presented

A link function approach to heterogeneous variance components

International audienc

Bayesian estimation of dispersion parameters with a reduced animal model including polygenic and QTL effects

International audienc