带有非线性边界条件的非齐次拟线性椭圆型方程组的多解性

Multiple Solutions for a Class of Quasilinear Nonhomogeneous Elliptic Systems with Nonlinear Boundary Conditions

主要研究一组带有非线性边界条件的非齐次拟线性椭圆型方程组非平凡解的存在性和多解性.利用山路引理和Ekeland变分准则,得到当λ属于特定区间时,此方程组至少存在两个非平凡解.

In this paper,we study the existence and multiplicity of nontrivial solutions for a class of quasilinear elliptic systems involving nonhomogeneous nonlinearities and nonlinear boundary conditions.By using the Mountain Pass Theorem and the Ekeland＇s variational principle,we prove that the system has at least two nontrivial solutions when the parameter A belongs to a certain subset of R.