The existence of infinitely many solutions at the first eigenvalue for a class of Dirichlet problems at a resonance is proved in two dimension by bifurcation theory. And the curve of solution intersects the eigenvalue line λ=λ1 infinitely many times.%主要是利用分歧理论,证明了在二维空间里,某一类Dirichlet共振问题在取第一特征值时,具有无穷多个解.解曲线与特征线λ=λ1无穷次相交.
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