Multiple solutions for a class of semilinear elliptic problems via Nehari-type linking theorem.

This paper is concerned with multiplicity results for semilinear elliptic equations of the type $$-\Delta u+a(x)u=\left| u\right| ^{p-2}u+f\left( x,u\right) $$ in $$\Omega $$ , $$u=0$$ on $$\partial \Omega $$ . We obtain at least two nontrivial solutions for this type of equations with the case that 0 is not a local minimizer of the corresponding functional under suitable hypotheses. The method we used here is based on a linking structure relevant to the Nehari manifold. [ABSTRACT FROM AUTHOR]