We study the existence and multiplicity of solutions for a class of quasilinear elliptic problem in exterior domain with Neumann boundary conditions

This article describes the classification of biodiesel samples using NIR spectroscopy and chemometric techniques. A total of 108 spectra of biodiesel samples were taken (being three samples each of four types of oil, cottonseed, sunflower, soybean and canola), from nine manufacturers. The measurements for each of the three samples were in the spectral region between 12,500 and 4000 cm(-1). The data were preprocessed by selecting a spectral range of 5000-4500 cm(-1), and then a Savitzky-Golay second-order polynomial was used with 21 data points to obtain second derivative spectra. Characterization of the biodiesel was done using chemometric models based on hierarchical cluster analysis (HCA), principal component analysis (PCA) and soft independent modeling of class analogy (SIMCA) elaborated for each group of biodiesel samples (cotton, sunflower, soybean and canola). For the HCA and PCA, the formation of clusters for each group of biodiesel was observed, and SIMCA models were built using 18 spectral measurements for each type of biodiesel (training set), and nine spectral measurements to construct a classification set (except for the canola oil which used eight spectra). The SIMCA classifications obtained 100% accurate identifications. Using this strategy, it was feasible to classify biodiesel quickly and nondestructively without the need for various analytical determinations.

We deal with the nonlinear Schrödinger equationwhere V is a (possible) sign changing potential satisfying mild assumptions and the nonlinearity f ∈ C 1 (R, R) is a subcritical and superlinear function. By combining variational techniques and the concentration-compactness principle we obtain a positive ground state solution and also a nodal solution. The proofs rely in localizing the infimum of the associated functional constrained to Nehari type sets.

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We study the existence of positive and negative weak solutions for the equationwhere ∆ p u = div(|∇u| p−2 ∇u) is the p-Laplacian operator, 1 < p < N , λ is a positive real parameter and the potential V : R N → R is bounded from below for a positive constant and "large" at infinity. It is assumed that the nonlinearity f : R → R is continuous and just superlinear in a neighborhood of the origin.

In this paper we study a class of nonhomogeneous Schrödinger equationsin the whole two-dimension space where V (x) is a continuous positive potential bounded away from zero and which can be "large" at the infinity. The main difficulty in this paper is the lack of compactness due to the unboundedness of the domain besides the fact that the nonlinear term f (s) is allowed to enjoy the critical exponential growth by means of the Trudinger-Moser inequality. By combining variational arguments and a version of the Trudinger-Moser inequality, we establish the existence of two distinct solutions when h is suitably small.

-Development of leaf spots resistant runner peanut cultivars is one of the major demands in

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