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In this paper, we study the multiplicity results of positive solutions for a semi-linear elliptic system involving both concave–convex and critical growth terms. With the help of the Nehari manifold and the Lusternik–Schnirelmann category, we investigate how the coefficient h(x)h(x) of the critical nonlinearity affects the number of positive solutions of that problem and get a relationship between the number of positive solutions and the topology of the global maximum set of hh.  相似文献   

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In this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system (Eλ,μ)(Eλ,μ) with sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ)(λ,μ) belongs to a certain subset of R2R2.  相似文献   

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We study the existence of multiple positive solutions for a superlinear elliptic PDE with a sign-changing weight. Our approach is variational and relies on classical critical point theory on smooth manifolds. A special care is paid to the localization of minimax critical points.  相似文献   

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We consider the semilinear elliptic problem in Ω, u=0 on ∂Ω, where 0∈Ω is a smooth bounded domain in RN, N?4, , is the critical Sobolev exponent, f(x,⋅) has subcritical growth at infinity, K(x)>0 is continuous. We prove the existence of sign-changing solutions under different assumptions when Ω is a usual domain and a symmetric domain, respectively.  相似文献   

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通过考察函数f,g在端点处的性质证明了一类非线性椭圆系统在环域上的正径向解的存在性.  相似文献   

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In this paper we consider the existence of nontrivial solutions for an elliptic system, where the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones and computing the fixed point index in K1, K2 and K1×K2, we obtain that the elliptic system has three nontrivial solutions (u,0), (0,v) and (u,v). It is remarkable that the third nontrivial solution (u,v) is established on the Cartesian product of two cones, in which the feature of two equations can be exploited better.  相似文献   

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In this article, we consider a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and one sign-changing function. The existence and multiplicity results of positive solutions are obtained by variational methods.  相似文献   

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We use the mountain pass theorem to study the existence and multiplicity of positive solutions of the generalisation of the well-known logistic equation -Δu=λg(x)u(x)(1-u(x))-Δu=λg(x)u(x)(1-u(x)) with Dirichlet boundary conditions to the case where g changes sign.  相似文献   

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In this paper, an elliptic system with boundary blow-up is considered in a smooth bounded domain. By constructing certain upper solution and subsolution, we show the existence of positive solutions and give a global estimate. Furthermore, the boundary behavior of positive solutions is also discussed.  相似文献   

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The present paper is concerned with a class of quasi-linear elliptic degenerate equations. The degenerate operator arises from analysis of manifolds with singularities. The variational methods are applied here to verify the existence of infinitely many solutions for the problem.

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In this work we study the existence and regularity of solutions of the equation Δ p 2 u = λm|u| q?2 u with the boundary conditions of Navier in the case pq.  相似文献   

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We study the existence of multiple solutions for a class of even-order nonlinear elliptic equations with the Dirichlet boundary conditions. We also study the corresponding nonlinear Hamiltonian system of higher-order linear equations.  相似文献   

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