Multiple positive solutions of superlinear elliptic problems with sign-changing weight
نویسندگان
چکیده
منابع مشابه
Superlinear elliptic problems with sign changing coefficients
Via variational methods, we study multiplicity of solutions for the problem −∆u = λb(x)|u|q−2u + a u + g(x, u) in Ω , u = 0 on ∂Ω . where a simple example for g(x, u) is |u|p−2u; here a, λ are real parameters, 1 < q < 2 < p ≤ 2∗ and b(x) is a function in a suitable space L. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any λ > 0, and a...
متن کاملMultiple Positive Solutions for Semilinear Elliptic Equations with Sign - Changing Weight Functions
and Applied Analysis 3 In order to describe our main result, we need to define Λ0 ( 2 − q ( p − q‖a‖L∞ ) 2−q / p−2 ( p − 2 ( p − q)‖b ‖Lq∗ ) S p 2−q /2 p−2 q/2 p > 0, 1.3 where ‖a‖L∞ supx∈RNa x , ‖b ‖Lq∗ ∫ RN |b x |qdx 1/q∗ and Sp is the best Sobolev constant for the imbedding of H1 R into L R . Theorem 1.1. Assume that a1 , b1 b2 hold. If λ ∈ 0, q/2 Λ0 , Ea,λb admits at least two positive solu...
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 کاملMultiple Positive Solutions for Quasilinear Elliptic Problems with Sign-changing Nonlinearities
Using variational arguments we prove some nonexistence and multiplicity results for positive solutions of a system of p−Laplace equations of gradient form. Then we study a p−Laplace type problem with nonlinear boundary conditions.
متن کاملMultiplicity of positive solutions for critical singular elliptic systems with sign - changing weight function ∗
In this paper, the existence and multiplicity of positive solutions for a critical singular elliptic system with concave and convex nonlinearity and sign-changing weight function, are established. With the help of the Nehari manifold, we prove that the system has at least two positive solutions via variational methods.
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 Differential Equations
سال: 2005
ISSN: 0022-0396
DOI: 10.1016/j.jde.2004.08.009