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Zbl 1196.34023
Heidarkhani, Shapour; Tian, Yu
Multiplicity results for a class of gradient systems depending on two parameters.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 2, 547-554 (2010). ISSN 0362-546X

Summary: We prove the existence of at least three solutions for a class of two-point boundary value systems of the type $$u_i''+u_i=\lambda F_{u_i}(x,u+1,\dots,u_n)+\mu G_{u_i}(x,u_1,\dots,u_n),\quad u_i'(a)=u_i'(b)=0$$ for $1\le i\le n$. The approach is fully based on a recent three critical points theorem of Ricceri.
MSC 2000:
*34B08 Multi-parameter boundary value problems
34B15 Nonlinear boundary value problems of ODE
47J10 Nonlinear eigenvalue problems
34B09 Boundary value problems with an indefinite weight

Keywords: three solutions; critical point; multiplicity results; double eigenvalue problem; Neumann problem

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