Multiple solutions for a semilinear problem with combined terms and nonlinear boundary conditions

作者：Furtado Marcelo F^*; Ruviaro Ricardo

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(14): 4820-4830.

DOI：10.1016/j.na.2011.04.054

• Variational methods
• Elliptic problems
• Sublinear and asymptotically linear
• Resonant problems

We consider the problem
-Lambda u + u = f (x, u) in Omega, partial derivative u/partial derivative eta = h(x)vertical bar u vertical bar(q-2)u on partial derivative Omega,
where Omega subset of R(N) is a smooth bounded domain, N >= 3, 1 <= q < 2 and h belongs to an appropriated Lebesgue space. In our main results, we suppose that f is an asymptotically linear function and we obtain multiplicity of solutions when the norm of h is small. We also present a multiplicity result in the case that f is nonquadratic at infinity.

• 出版日期2011-10