EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR SOME SEMILINEAR ELLIPTIC EQUATIONS IN ANNULUS

Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.

A NOTE ON THE UNIQUENESS AND THE NON-DEGENERACY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS AND ITS APPLICATION

In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE anal- ysis, we extend previous results to cases where nonlinear terms may have sublinear growth. As an application, we obtain the uniqueness and the non-degeneracy of ground states for modified SchrSdinger equations.

Several Existence Theorems for Positive Radial Solutions to a Semilinear Elliptic BVP

The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist.

EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR SINGULAR ELLIPTIC SYSTEMS

The existence of positive radial solutions to the systems of m(m≥1) semilinear elliptic equations Δu+p(r)f(u)=0,0<A<r<B in annuli with Dirichlet(Dirichlet/Neumann)boundary conditions,is studied,where r=x 2 1+...+x 2 n,n≥1.u=(u 1,...,u m),p(r)f(u)=(p 1(r)f 1(u),...,p m(r)f m(u)), and p(r) may be singular at r=A or r=B,f may be singular at u=0.

Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball

In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP: , where Δu = div (∇u) and Δv = div (∇v) are the Laplacian of u, λ is a positive parameter, Ω = {x ∈ Rn : N > 2, |x| > r0, r0 > 0}, let i = [1,2] then Ki :[r0,∞] → (0,∞) is a continuous function such that limr→∞ ki(r) = 0 and is The external natural derivative, and : [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of f with a) fi > 0, b) fi < 0, and c) fi = 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings.

NON-EXISTENCE OF POSITIVE ENTIRE SOLUTIONS FOR ELLIPTIC INEQUALITIES OF P-LAPLACIAN

In this paper, the nonexistence of positive entire solutions for div(|Du| p-2 Du)q(x)f(u),x∈R N, is established, where p】1,Du=(D 1u,...,D Nu),q∶R N→(0,∞) and f∶(0,∞)→(0,∞) are continuous functions.

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO CERTAIN QUASILINEAR ELLIPTIC EQUATIONS IN A BALL

By the fixed point theorem on a cone and monotone iterativc technique, the existence and multiplicity of the positive radial solutions to a class of quasilinear elliptic equations are considered. Also, using the monotone iteration method the authors deal with the boundary value problem as the nonlinear term f（t, u） increases in u.

Asymptotic Behavior of Nodal Solutions for Semilinear Elliptic Equationsin R^n

In this paper,we have investigated the asymptotic behavior of nodal solutions of semilinear elliptic equations in R n. We conclude more precise and extensive results and give the expression of asymptotic behavior near ∞ more detail than that of [3]-[5].

EXISTENCE OF POSITIVE RADIAL SOLUTIONS AND ENTIRE SOLUTIONS FOR QUASILINEAR SINGULAR BOUNDARY VALUE PROBLEMS

In this paper, we establish the existence of positive radially symmetric solutions of div(|Du|p-2Du) + λf(r,u(r) ) = 0 in domain R1 < r < R0 or 0 < r < ∞ with a variety of Dirichlet boundary conditions. The function f is allowed to be singular when u = 0.

EXISTENCE AND NONEXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS

In this paper an existence theorem of positive radial solutions to a class of semilinear elliptic systems is proved by the Leray-Schauder degree theorem. Also, a nonexistence theorem is obtained. As an application of the main theorem, an example is given.

EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS

Existence and multiplicity results of positive radially symmetric solution ofthe eigenvalue problemsare obtained for fi being a N-ball or an annulus via Leray-Schauder degreetheory and variational method.

PERTURBATION METHODS IN SEMILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENT

In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory.

Some Uniqueness Results for a Class of Quasilinear Elliptic Eigenvalue Problems

Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved that there is no non-radial positive solution.