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Dragos-Patru Covei

Publications and source records attributed to Dragos-Patru Covei.

44 records · Page 3Linked to original sources
arXiv2011

Existence results for a quasilinear elliptic problem with a gradient term via shooting method

In this paper we obtain the existence of bounded positive entire radial solutions for the following nonlinear elliptic problem with a special nonlinear gradient term -\triangle_{p}u-b(x)|\nablau|^{p-1}=a(x)f(u), x\inR^{N} (N\geq3), lim_{|x|\rightarrow \infty}u(x)=0, where \triangle_{p}u=div[big] \big( |\nablau|^{p-2}\nablau[big] \big) , 1<p<N, a(x)=a(|x|), b(x)=b(|x|) which are continuous, and f\inC^1(0,\infty) which may be singular at zero.

math.AP↗
arXiv2011

Quasilinear Problems with the Competition Between Convex and Concave Nonlinearities and Variable Potentials

The purpose of this paper is to prove some existence and non-existence theorems for the nonlinear elliptic problems of the form -Δ_{p}u=λk(x)u^{q}\pmh(x)u^{σ} if x\inΩ, subject to the Dirichlet conditions u_{1}=u_{2}=0 on \partialΩ. In the proofs of our results we use the sub-super solutions method and variational arguments. Related results as obtained here have been established in [Z. Guo and Z. Zhang, W^{1,p} versus C^{1} local minimizers and multiplicity results for quasilinear elliptic equations, Journal of Mathematical Analysis and Applications, Volume 286, Issue 1, Pages 32-50, 1 October 2003.] for the case k(x)=h(x)=1. Our results reveal some interesting behavior of the solutions due to the interaction between convex-concave nonlinearities and variable potentials.

math.CA↗
arXiv2011

An existence result for a quasilinear system with gradient term under the Keller-Osserman conditions

We deal with existence of entire solutions for the quasilinear elliptic system of this type Δ_{p}u_{i}+h_{i}(|x|)|\bigtriangledown u_{i}|^{p-1}=a_{i}(|x|)f_{i}(u_1,u_2) on R^{N} (N\geq3, i=1,2) where N-1\geqp>1, Δ_{p} is the p-Laplacian operator and h_{i}, a_{i}, f_{i} are suitable functions. The results of this paper supplement the existing results in the literature and improve those obtained by Xinguang Zhang and Lishan Liu, The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term, Journal of Mathematical Analysis and Applications, Volume 371, Issue 1, 1 November 2010, Pages 300-308).

math.CA↗
arXiv2011

Radial solutions for a quasilinear elliptic system of Schrödinger type

In this paper we analyze the existence of entire radially symmetric solutions for Schrodinger system type Δ_{p_{i}}u_{i}+h_{i}(r)|\nabla u_{i}|^{p_{i}-1}=a_{i}(r)f_{i}(u_1,...,u_{d}) for i=1,...,d on R^{N} where p_{i}>1, d \in {1,2,3,...}, h_{i} and a_{i} are nonnegative radial continuous functions and f_{i} are nonnegative increasing continuous functions on [0,\infty).

math.CA↗
arXiv2011

Radial and nonradial solutions for a semilinear elliptic system of Schrödinger type

In this article we consider the system of equations Δu_{i}=p_{i}(x)f_{i}(u_{1},...,u_{d}) for i=1,...,d on R^{N}, N\geq3 and d\in{1,2,3,4,...}. We prove that the considered system has a bounded positive entire solution under some conditions on p_{i} and f_{i}. Also, we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation. Furthermore, a non-radially symmetric solution is obtained by using a lower and upper solution method.

math.AP↗