SMOOTH POSITIVE SOLUTIONS TO AN ELLIPTIC MODEL WITH $C^{2}$ FUNCTIONS
نویسندگان
چکیده
منابع مشابه
Multiple 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 کاملSmooth approximations to solutions of nonconvex fully nonlinear elliptic equations
We show that fully nonlinear elliptic PDEs (which may not have classical solutions) can be approximated with integro-differential equations which have C solutions. For these approximated equation we prove a uniform C estimate. We also study the rate of convergence.
متن کاملExistence and regularity of positive solutions for an elliptic system ∗
In this paper, we study the existence and regularity of positive solution for an elliptic system on a bounded and regular domain. The non linearities in this equation are functions of Caratheodory type satisfying some exponential growth conditions.
متن کاملPositive Solutions of Quasilinear Elliptic Equations
(1.2) { −∆pu = λa(x)|u|p−2u, u ∈ D 0 (Ω), has the least eigenvalue λ1 > 0 with a positive eigenfunction e1 and λ1 is the only eigenvalue having this property (cf. Proposition 3.1). This gives us a possibility to study the existence of an unbounded branch of positive solutions bifurcating from (λ1, 0). When Ω is bounded, the result is well-known, we refer to the survey article of Amann [2] and t...
متن کاملPositive Solutions of Elliptic Equations withSingular
In this paper, a nonlinear elliptic boundary value problem with singular nonlinearity is studied, where L is a uniformly elliptic operator, is a bounded domain in R N , N 2, 0 may take the value 0 on @, and f(x; s) is possibly singular near s = 0. Some results regarding the existence of positive solutions for the problem are given under a set of hypotheses that make neither monotonicity nor str...
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: International Journal of Pure and Apllied Mathematics
سال: 2015
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v105i4.7