Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient

In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution set. Our approach is based on Leray-Schauder alternative principle, method of sub-supersolution, nonlinear regularity, truncation techniques, and set-valued analysis

Existence of continuous eigenvalues for a class of parametric problems involving the (p,2)-laplacian operator

We discuss a parametric eigenvalue problem, where the differential operator is of (p,2)-Laplacian type. We show that, when p≠2, the spectrum of the operator is a half line, with the end point formulated in terms of the parameter and the principal eigenvalue of the Laplacian with zero Dirichlet boundary conditions. Two cases are considered corresponding to p>2 and p2, and to infinity in the case of p<2

Vehicle designing with application of quality standards

Normy serii ISO 9000 i inne normy związane z zarządzaniiem jakością są wprowadzane po to, żeby różnym organizacjom ułatwić zarządzanie wszystkimi funkcjami, które mają wpływ na jakość ich wyrobów, a w tym także projektowania. Model zarządzania jakością projektowania według ISO preferuje tzw. podejście procesowe i obliguje do wprowadzania pewnych działań porządkujących i kontrolnych (planowanie jakości, przegląd wymagań, planowanie projektowania, przegląd projektowania, walidacja). Znormalizowane systemy zarządzania nie naruszają naukowych i praktycznych zasad projektowania, ale je lepiej organizują i dyscyplinują.The ISO 9000 family of standards and other standards of quality management are introduced to make the management of functions in different organizations easier. Those functions have an impact on the quality of products, including processes of design. The process' approach is preferred by the ISO model of quality ofdesign. This model also obliges the introduction of sorting and controlling activities, including quality planning, survey of requirements, planning and designing, survey of designing, and validation. The quality management systems are compatible with theoreticalk and practical rules of designing. Moreover, the management systems have an influence on those rules, organizing and determining them in a better way

A pair of positive solutions for the Dirichlet p(z)-Laplacian with concave and convex nonlinearities

We consider a nonlinear parametric Dirichlet problem driven by the anisotropic p-Laplacian with the combined effects of “concave” and “convex” terms. The “superlinear” nonlinearity need not satisfy the Ambrosetti-Rabinowitz condition. Using variational methods based on the critical point theory and the Ekeland variational principle, we show that for small values of the parameter, the problem has at least two nontrivial smooth positive solution