On the existence of positive solutions for semilinear elliptic equations with indefinite nonlinearities

In this paper, we study the existence of positive solutions for the semilinear elliptic problem

     

Eigenvalues in Non-Linear Potential Theory

In this work, we study the existence of eigenvalues for a type of non-linear equations and we give some conditions to get positive eigenfunctions. Particularly, we show that under some appropriate conditions, the set of eigenvalues is an interval.     

LOWER BOUNDS FOR SUP＋INF AND SUP＊INF AND AN EXTENSION OF CHEN-LIN RESULT IN DIMENSION 3

We give two results about Harnack type inequalities. First, on Riemannian surfaces, we have an estimate of type sup ＋ inf. The second result concern the solutions of prescribed scalar curvature equation on the unit ball of Rn with Dirichlet condition. Next, we give an inequality of type （supK ^u）^2s-1 × infπu ≤ c for positive solutions of △u = V u^5 on Ω belong toR^3, where K is a compact set of Ω and V is s-Holderian, s ∈] - 1/2, 1]. For the case s = 1/2 and Ω = S3, we prove that, if minΩ u 〉 m 〉 0 （for some particular constant m 〉 0）, and the H¨olderian constant A of V tends to 0 （in certain meaning）, we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set of Ω.     

A uniform estimate for scalar curvature equation on manifolds of dimension 4

We consider the solutions to the prescribed scalar curvature equation on a four-dimensional Riemannian manifold M. We prove an upper bound for the supremum of all the solutions on every compact subset K of M, provided that all the solutions on M are bounded from below by a positive number.     

Synthesis and X-ray structure of cationic methallyl palladium complexes supported by unsymmetrical β-diimine ligands

Treatment of the unsymmetrical β-iminoamine ligands [PhCN(Ar)CHCNH(Ar)Me] with the zerovalent complex Pd(dba)₂ in the presence of the methallyloxyphosphonium salt, gives high yields of the cationic β-diimine complexes [PhCN(Ar)CH₂CN(Ar)(Me)Pd(η³-C₄H₇)]⁺[PF₆]⁻ (Ar = 2-Me-C₆H₄ (7); 2-MeO-C₆H₄ (8); 2,6-Me₂-C₆H₃ (9); 2,6-iPr₂-C₆H₃ (10)). All the new complexes have been characterised by NMR and IR spectroscopy. The structure of the cationic methallyl palladium complex (10) has been solved by X-ray crystallography.