Quasilinear

The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane-Emden type, including the following two model problems: −∆p u = uq + µ, Fk [−u] = uq + µ, u ≥ 0, on Rn , or on a bounded domain Ω ⊂ Rn . Here ∆p is the p-Laplacian defined by ∆p u = div ( u| u|p−2 ), and Fk [u] is the k-Hessian defined as the sum of k × k principal minors of the Hessian matrix D2 u (k = 1, 2, . . . ,...

58p dontetvui 17-01-2013 58 10   Download

This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data. The new results obtained here are sharp in low dimension. 1. Introduction 1.1. The results. We consider in this paper second order, nonlinear hyperbolic equations of the form (1.1) gij (u) ∂i ∂j u = q ij (u) ∂i u ∂j u on R × Rn , with Cauchy data prescribed at time 0, (1.2) u(0, x) = u0 (x) , ∂0 u(0, x) = u1 (x) .

77p noel_noel 17-01-2013 71 5   Download

MULTIPLE SOLUTIONS FOR QUASILINEAR ELLIPTIC NEUMANN PROBLEMS IN ORLICZ-SOBOLEV SPACES NIKOLAOS HALIDIAS AND VY K. LE Received 15 October 2004 and in revised form 21 January 2005 We investigate the existence of multiple solutions to quasilinear elliptic problems containing Laplace like operators (φ-Laplacians). We are interested in Neumann boundary value problems and our main tool is Br´ zis-Nirenberg’s local linking theorem. e 1. Introduction In this paper, we consider the following elliptic problem with Neumann boundary condition, −div α ∇u(x) ∇u(x) = g(x,u) a.e. on Ω (1.1) ∂u = 0 a.e.

8p sting12 10-03-2012 27 2   Download

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR p-LAPLACIAN PROBLEMS BY VARIATIONAL METHODS KANISHKA PERERA AND ZHITAO ZHANG Received 20 July 2004 We obtain multiple positive solutions of singular p-Laplacian problems using variational methods. The techniques are applicable to other types of singular problems as well. 1. Introduction We consider the singular quasilinear elliptic boundary value problem −∆ p u = a(x)u−γ + λ f (x,u) in Ω, (1.1) u 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded C 2 domain in Rn ,n ≥ 1, ∆ p u = div(|∇u| p−2 ∇u) is the p-Laplacian, 1 0 is a constant, λ...

6p sting12 10-03-2012 44 3   Download

THE FIRST EIGENVALUE OF p-LAPLACIAN SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS D. A. KANDILAKIS, M. MAGIROPOULOS, AND N. B. ZOGRAPHOPOULOS Received 12 October 2004 and in revised form 21 January 2005 We study the properties of the positive principal eigenvalue and the corresponding eigenspaces of two quasilinear elliptic systems under nonlinear boundary conditions. We prove that this eigenvalue is simple, unique up to positive eigenfunctions for both systems, and isolated for one of them. 1. Introduction Let Ω be an unbounded domain in RN , N ≥ 2, with a noncompact and smooth boundary ∂Ω.

15p sting12 10-03-2012 51 4   Download

ROTHE TIME-DISCRETIZATION METHOD APPLIED TO A QUASILINEAR WAVE EQUATION SUBJECT TO INTEGRAL CONDITIONS ABDELFATAH BOUZIANI AND NABIL MERAZGA Received 27 January 2004 and in revised form 12 February 2004 This paper presents a well-posedness result for an initial-boundary value problem with only integral conditions over the spatial domain for a one-dimensional quasilinear wave equation. The solution and some of its properties are obtained by means of a suitable application of the Rothe time-discretization method. 1.

25p sting12 10-03-2012 39 7   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

8p dauphong18 09-03-2012 34 2   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: EXISTENCE AND NONEXISTENCE OF POSITIVE SOLUTIONS FOR QUASILINEAR SYSTEMS

9p dauphong18 09-03-2012 47 4   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: GENERALIZED QUASILINEARIZATION METHOD AND HIGHER ORDER OF CONVERGENCE FOR SECOND-ORDER BOUNDARY VALUE PROBLEMS

15p dauphong18 09-03-2012 41 4   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Nonexistence of Positive Solution for Quasilinear Elliptic Problems in the Half-Space

4p dauphong18 09-03-2012 48 2   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: OSCILLATION AND NONOSCILLATION THEOREMS FOR A CLASS OF EVEN-ORDER QUASILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

22p dauphong18 09-03-2012 42 4   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence and Nonexistence Results for a Class of Quasilinear Elliptic Systems

5p sting10 24-02-2012 34 4   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Systems of Quasilinear Parabolic Equations with Discontinuous Coefficients and Continuous Delays

25p dauphong13 09-02-2012 57 7   Download