Extrema problems with critical sobolev exponents on unbounded domains

Positive and Nodal Solutions For a Nonlinear Schrödinger Equation with Indefinite Potential

“…Moreover, we may have V ∈ L N/2 (R N ) and therefore Theorem 1.1 also complements the results of [23,7].…”

“…where ε > 0 is small and 0 < α < 2, satisfies our hypotheses but the arguments of [23,7,24,11] do not apply for this potential. Finally, we would like to cite the recent papers [15,16], where the authors have considered a singularly perturbed version of (P ) and have obtained some results related, but not comparable, with ours.…”

“…Lions [20], conditions like (V 1 ) have appeared in many works with positive or sign changing potentials [29,23,9,11,7]. Some conditions related to (V 2 ) have already appeared in [5,24,11,12,6] where the authors considered problem (P ) or some of its variants.…”

Principal eigenvalue in an unbounded domain with indefinite potential

“…, and using (3.2) we obtain 4) so that A λ is coercive on W g+m2 for any λ > 0. Arguing as in the proof of Theorem 3.1, one deduces that for any λ > 0, (3.3) has a principal eigenvalue…”

Perturbations near resonance for the p‐Laplacian in ℝN

“…In addition, the critical points of J λ are precisely the weak solutions of (1.1). Next we recall a compactness result which is proved in [5].…”