The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function

A multiplicity result for a singular problem with subcritical nonlinearities

“…To obtain multiple (at least two distinct, positive) solutions of problem (P λ ), we combine some well-known fibering maps (i.e., maps of the form t → E λ (tu), see (ALVES-EL HAMIDI [1], BROWN-ZHANG [2]) and minimization on the suitable subset of Nehari manifold.…”

Multiple positive solutions of semilinear elliptic equations involving concave and convex nonlinearities in ℝ N

“…They proved that this equation has at least two positive solutions for sufficiently small c > 0. More general results of Equation (E c ) were done by Ambrosetti et al [3], Brown and Zhang [4], and de Figueiredo et al [5].…”

A remark on the existence and multiplicity result for a nonlinear elliptic problem involving the p-Laplacian

“…In recent years, several authors use the Nehari manifold to solve semilinear and quasilinear problems (see [1,[8][9][10][11][20][21][22]). Brown and Zhang [11] have studied the following subcritical semilinear elliptic equation with a sign-changing weight function…”

“…Brown and Zhang [11] have studied the following subcritical semilinear elliptic equation with a sign-changing weight function…”

“…Recently, in [8], the author considered the above problem with a ≡ 1 and 1 < γ < 2. In this work, we give a variational method which is similar to the fibering method (see [12] or [11]) to prove the existence of at least two nontrivial nonnegative solutions of problem (1). In particular, by using the method of [10], we do this without the extraction of the Plais-Smale sequences in the Nehari manifold as in [1,20].…”