Abstract
In this paper, using Local Linking Theorem, we obtain the existence of multiple solutions for a class of semilinear elliptic equations with nonlinear boundary conditions, in which the nonlinearites are compared with higher Neumann eigenvalue and the first Steklov eigenvalue.
Highlights
Using sub and super-solutions method, Amann (see [3]), Mawhin and Schmitt (see [4]) obtained some existence results for the problem (1.1)
We investigate the multiple solutions for semilinear elliptic equation with nonlinear boundary conditions
In this paper, using the Local Linking Theorem, we obtain multiple solutions for the problem (1.1), which the nonlinearites are compared with higher Neumann eigenvalue and the first Steklov eigenvalue
Summary
Using sub and super-solutions method, Amann (see [3]), Mawhin and Schmitt (see [4]) obtained some existence results for the problem (1.1). In this paper, using the Local Linking Theorem, we obtain multiple solutions for the problem (1.1), which the nonlinearites are compared with higher Neumann eigenvalue and the first Steklov eigenvalue. As the function c x satisfies the condition C), we define the weighted As the function c(x) satisfies the condition C), by Equation (2.2), we can split
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