id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-39	Il'yasov, Yavdat; da Silva, Edcarlos Domingos; da Silva, Maxwell Lizete	Prescribed energy saddle-point solutions of nonlinear indefinite problems	2023	11	.pdf	application/pdf	5440	316	78	Then u = (u+ + u−) ∈ W, u± ∈ W±, and c0‖u‖21 ≤ ‖u‖2W ≤ c1‖u‖21, ∀u ∈ W , where 0 < c0, c1 < +∞ do not depend on u ∈ W . This by the Sobolev inequalities implies∫ G(x, u)dx ≤ ε 2 C1‖u‖21 + C2(ε)‖u‖γ1 , u ∈W, (3.1) 6 Y. IL’YASOV, E. D. SILVA, M. L. SILVA EJDE-2023/23 where C1, C2(ε) ∈ (0,+∞) do not depend on u ∈ W and C1 does not depend on ε > 0.	cache/ejde-39.pdf	txt/ejde-39.txt