一类双调和方程的非平凡解的存在性

Existence of nontrivial solutions for a class of biharmonic equations

利用山路引理,讨论了非线性项在负无穷远处是渐近线性而在正无穷远处是超线性的一类双调和方程,且获得了该方程的非平凡解.所得结论推广了文献[3]和文献[5]的相应定理.

By using the Mountain pass Lemma, when the nonlinear term is asymptotically linear at the negative infinity but superlinear at the positive infinity, a class of biharmonic equations at resonance are discussed. The existence of nontrivial solutions is proved. The resevant theorems of the literature [-3] and [-5] are generalized.