Multiple Positive Solutions for Some Nonlinear Elliptic Systems
نویسندگان
چکیده
where k1, k2 > 0 are positive constants, Ω ⊂ R is a bounded domain with a smooth boundary ∂Ω and V (u, v) ∈ C(R,R). We refer to [CdFM], [CM], [dFF], [dFM] and [HvV] for variational study of such elliptic systems. However, it seems that the multiplicity of positive solutions for such elliptic systems is not well studied. Here, we study a case related to some models (with diffusion) in mathematical biology, ecology, etc., and we consider the case where (0.1)–(0.3) have 4 constant non-negative solutions (0, 0), (a, 0), (0, b), (u0, v0) ∈ R (a, b, u0, v0 > 0), that is, solutions of Vu(u, v) = Vv(u, v) = 0, and 2 constant solutions (a, 0), (0, b) are
منابع مشابه
Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.
متن کاملThe Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
متن کاملExistence of Positive Radial Solutions for Some Nonlinear Elliptic Systems
In this paper we study a class of nonvariational elliptic systems, by using the Gidas-Spruck Blow-up method. first, we obtain a priori estimates, and then using Leray-Schauder topological degree theory, we establish the existence of positive radial solutions vanishing at infinity.
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 کاملExistence of at least three weak solutions for a quasilinear elliptic system
In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...
متن کامل