Existence and multiplicity results are obtained for superlinear p-Laplacian equations without the Ambrosetti and Rabinowitz condition. To overcome the difficulty that the Palais-Smale sequences of the EulerLagrange functional may be unbounded, we consider the Cerami sequences. Our results extend the recent results of Miyagaki and Souto [ J. Differential Equations 245 (2008), 3628–3638].

This paper describes optimization of the Takagi-Sugeno fuzzy model. To prove the existence of optimal control, we apply compactness of a set of membership functions in L space and continuity of approximate reasoning and show the existence of a pair of membership functions which minimize the quadratic performance function.

This paper presents an approach to texture segmen tation by thresholding based on compactness measures of fuzzy sets to determine thresholds of an ill-defined image. The extension of fuzziness in the texture feature space provides more meaningful results than by considering fuzziness in gray scale domain. The effectiveness of the algorithm is demonstrated by comparison with other traditional no...

This work lies within the scope of color image segmentation by pixel classification. The classes of pixels are constructed by detecting the modes of the spatial-color compactness function, which characterizes the image by taking into account both the distribution of colors in the color space and their spatial location in the image plane. A fuzzy transformation of this function is performed, bas...

This paper presents an improved method for image thresholding by optimization of fuzzy compactness which was originally introduced by Pal and Rosenfeld 3]. In our method a set of asymmetric S-functions whose windows are located in the same range are used as membership functions for obtaining fuzzy compact-ness. This avoids the problem which may occur in the original algorithm by unsuitably choo...