Weak Solutions of Nonlinear Elliptic Equations with Prescribed Singular Set
نویسندگان
چکیده
منابع مشابه
Existence of Positive Weak Solutions with a Prescribed Singular Set of Semilinear Elliptic Equations
In this paper, we consider the problem of the existence of non-negative weak solution u of A u + u P = O i n ~ u = 0 on Of~ n n + 2 ~ / n 1 having a given closed set S as its singular set. We prove that when < p < _ _ and n 2 n 4 + 2 nv/'n-L--1 S is a closed subset of f2, then there are infinite many positive weak solutions with S as their singular set. Applying this method to the conformal sca...
متن کاملSingular Radial Entire Solutions and Weak Solutions with Prescribed Singular Set for a Biharmonic Equation
Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular ...
متن کاملSome remarks on singular solutions of nonlinear elliptic equations. I
We study strong maximum principles for singular solutions of nonlinear elliptic and degenerate elliptic equations of second order. An application is given on symmetry of positive solutions in a punctured ball using the method of moving planes. Mathematics Subject Classification (2000). 35J69, 58J05, 53C21, 35J60.
متن کاملExistence of Positive Weak Solutions for Fractional Lane–emden Equations with Prescribed Singular Sets
In this paper, we consider the problem of the existence of positive weak solutions of { (−∆)su = up in Ω u = 0 on Rn\Ω having prescribed isolated interior singularities. We prove that if n n−2s < p < p1 for some critical exponent p1 defined in the introduction which is related to the stability of the singular solution us, and if S is a closed subset of Ω, then there are infinitely many positive...
متن کاملExistence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight
This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight. We apply the variational methods to prove the existence of ground state solution.
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: 1996
ISSN: 0022-0396
DOI: 10.1006/jdeq.1996.0077