On sign-changing and multiple solutions of the p-Laplacian
نویسندگان
چکیده
منابع مشابه
SIGN-CHANGING AND MULTIPLE SOLUTIONS FOR THE p-LAPLACIAN SIEGFRIED CARL AND KANISHKA PERERA
where ∆pu= div(|∇u|p−2∇u) is the p-Laplacian, 1 < p <∞. ByW1,p(Ω) we denote the usual Sobolev space with dual space (W1,p(Ω))∗, andW 0 (Ω) denotes its subspace whose elements have generalized homogeneous boundary values and whose dual space is given by W−1,p(Ω). We assume the following growth and asymptotic behaviour of the nonlinear right-hand side f of (1.1): (H1) f :Ω×R → R is a Carathéodory...
متن کاملExistence of multiple positive solutions for a p-Laplacian system with sign-changing weight functions
A p-Laplacian system with Dirichlet boundary conditions is investigated. By analysis of the relationship between the Nehari manifold and fibering maps, we will show how the Nehari manifold changes as λ,μ varies and try to establish the existence of multiple positive solutions. c © 2007 Elsevier Ltd. All rights reserved.
متن کاملMultiplicity of Positive Solutions of laplacian systems with sign-changing weight functions
In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.
متن کاملPositive solutions of singular p-Laplacian BVPs with sign changing nonlinearity on time scales
We investigate a class of singular m-point p-Laplacian boundary value problem on time scales with the sign changing nonlinearity. By using the well-known Schauder fixed point theorem and upper and lower solutions method, some new existence criteria for positive solutions of the boundary value problem are presented. These results are new even for the corresponding differential (T = R) and differ...
متن کاملMONOTONE POSITIVE SOLUTIONS FOR p-LAPLACIAN EQUATIONS WITH SIGN CHANGING COEFFICIENTS AND MULTI-POINT BOUNDARY CONDITIONS
We prove the existence of three monotone positive solutions for the second-order multi-point boundary value problem, with sign changing coefficients, [p(t)φ(x′(t))]′ + f(t, x(t), x′(t)) = 0, t ∈ (0, 1), x′(0) = − l X i=1 aix (ξi) + m X i=l+1 aix (ξi), x(1) + βx′(1) = k X i=1 bix(ξi)− m X i=k+1 bix(ξi)− m X i=1 cix (ξi). To obtain these results, we use a fixed point theorem for cones in Banach s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2003
ISSN: 0022-1236
DOI: 10.1016/s0022-1236(02)00103-9