Multiple solutions for p-Laplacian type problems with asymptotically p-linear terms via a cohomological index theory

作者：Candela A M^*; Palmieri G; Perera K

来源：Journal of Differential Equations, 2015, 259(1): 235-263.

DOI：10.1016/j.jde.2015.02.007

• p-Laplacian type equation
• Asymptotically p-linear problem
• Palais-Smale condition
• Cohomological index theory
• Pseudo-index theory

The aim of this paper is investigating the existence of weak solutions of the quasilinear elliptic model problem
{-div(A(x,u) vertical bar del u vertical bar(p-2)del u) + 1/p A(t)(x,u) vertical bar del u vertical bar(p) = f(x, u) in Omega, u = 0 on partial derivative Omega,
where Omega subset of R-N is a bounded domain, N >= 2, p > 1, A is a given ftmction which admits partial derivative A(t) (x, t) = partial derivative A/partial derivative t(x, t) and f is asymptotically p-linear at infinity.
Under suitable hypotheses both at the origin and at infinity, and if A(x,.) is even while f (x,.) is odd, by using variational tools, a cohomological index theory and a related pseudo-index argument, we prove a multiplicity result if p > N in the non-resonant case.

• 出版日期2015-7-5