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We prove the existence of nonconstant positive solutions for a system of the form , in , with Neumann boundary conditions on , where is a smooth bounded domain and , are power-type nonlinearities having superlinear and subcritical growth at infinity. For small values of , the corresponding solutions and admit a unique maximum point which is located at the boundary of .

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2.
Perturbation from symmetry for indefinite semilinear elliptic equations   总被引:1,自引:0,他引:1  
We prove the existence of an unbounded sequence of solutions for an elliptic equation of the form -Du=lu + a(x)g(u)+f(x), u ? H10(W){-\Delta u=\lambda u + a(x)g(u)+f(x), u\in H^1_0(\Omega)}, where l ? \mathbbR, g(·){\lambda \in \mathbb{R}, g(\cdot)} is subcritical and superlinear at infinity, and a(x) changes sign in Ω; moreover, g( − s) =  − g(s) "s{\forall s}. The proof uses Rabinowitz’s perturbation method applied to a suitably truncated problem; subsequent energy and Morse index estimates allow us to recover the original problem. We consider the case of W ì \mathbbRN{\Omega\subset \mathbb{R}^N} bounded as well as W = \mathbbRN,  N\geqslant 3{\Omega=\mathbb{R}^N, \, N\geqslant 3}.  相似文献
3.
We consider a system of the form in Ω with Neumann boundary condition on ∂Ω, where Ω is a smooth bounded domain in and f,g are power-type nonlinearities having superlinear and subcritical growth at infinity. We prove that the least energy solutions to such a system concentrate, as ε goes to zero, at a point of the boundary which maximizes the mean curvature of the boundary of Ω.  相似文献
4.
The authors extend some well-known Morse estimates for critical points of saddle point type to some linking conditions recently considered in the literature. Applications are given for multiplicity results in PDE and existence of subharmonic solutions for a class of conservative ODE. Research supported by Program STRIDE (contract STRDA/C/CEN/531/92) and EC (contract ERBCHRXCT940555).  相似文献
5.
We study the existence, multiplicity and shape of positive solutions of the system −ε2Δu+V(x)u=K(x)g(v), −ε2Δv+V(x)v=H(x)f(u) in RN, as ε→0. The functions f and g are power-like nonlinearities with superlinear and subcritical growth at infinity, and V, H, K are positive and locally Hölder continuous.  相似文献
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We correct the statement and the proof of Proposition 9 in [D. Bonheure, M. Ramos, Multiple critical points of perturbed symmetric strongly indefinite functionals, http://dx.doi.org/10.1016/j.anihpc.2008.06.002].  相似文献
8.
We consider a system of the form , in an open domain of , with Dirichlet conditions at the boundary (if any). We suppose that f and g are power-type non-linearities, having superlinear and subcritical growth at infinity. We prove the existence of positive solutions and which concentrate, as , at a prescribed finite number of local minimum points of V(x), possibly degenerate.  相似文献
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