Existence of multiple solutions to an elliptic problem with measure data
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Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Func. Anal. 14, 349–381 (1973)
Bachman, G., Narici, L.: Functional analysis(. Dover Publications, Mineola (1966)
Molica Bisci, G., Repovš, D., Servadei, R.: Nontrivial solutions of superlinear nonlocal problems. Forum Math 28(6), 1095–1110 (2016)
Boccardo, L., Gallouët, T.: Nonlinear elliptic equations with right hand side measures. Comm. Partial Differ. Equ. 17(3–4), 641–655 (1992)
Brezis, H., Marcus, M., Ponce, A.C.: Nonlinear elliptic equations with measures revisited. arXiv:1312.6495 [math.AP] (2013)
Chung, N.T., Minh, P.H., Nga, T.H.: Multiple solutions for $$p$$ p -Laplacian problems involving general subcritical growth in bounded domains. Electon. J. Differ. Equ. 78, 1–12 (2016)
Costa, D.G., Magalhães, C.A.: Variational elliptic problems which are nonquadratic at infinity. Nonlinear Anal. 23, 1401–1412 (1994)
Ercole, G., Pereira, G.A.: Fractional Sobolev inequalities associated with singular problems. Math. Nachr. https://doi.org/10.1002/mana.201700302 (2017)
Evans, L.C.: Partial differential equations. Graduate studies in mathematics, vol 19. American Mathematical Society (2009)
Bénilan, P., Boccardo, L., Gallouët, T., Gariepy, R., Pierre, M., Vazquez, J.L.: An $$L^1$$ L 1 theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa 22, 241–273 (1995)
Ge, B., Zhou, Q., Zu, L.: Positive solutions for nonlinear elliptic problems of p-Laplacian type on $$\mathbb{R}^{N}$$ R N without (AR) condition. Nonlinear Anal. 21, 99–109 (2015)
Giri, R.K., Choudhuri, D.: A problem involving the $$p$$ p -Laplacian operator. Differ. Equ. Appl. 9(2), 171–181 (2017)
Iturriaga, L., Lorca, S., Ubilla, P.: A quasilinear problem without the Ambrosetti-Rabinowitz type condition. Proc. R. Soc. Edinb. Sect. A 140, 391–398 (2010)
Kesavan, S.: Topics in functional analysis and applications. New Age International Pvt. Ltd. (2003)
Kristály, A., Lisei, H., Varga, C.: Multiple solutions for $$p$$ p -Laplacian type equations. Nonlinear Anal. TMA 68, 1375–1381 (2008)
Lan, Y.Y.: Existence of solutions to $$p$$ p -Laplacian equations involving general subcritical growth. Electr. J. Diff. Equ. 2014(151), 1–9 (2014)
Lan, Y.Y., Tang, C.L.: Existence of solutions to a class of semilinear elliptic equations involving general subcritical growth. Proc. R. Soc. Edinb. Sect. A 144, 809–818 (2014)
Liu, S.: On superlinear problems without Ambrosetti–Rabinowitz condition. Nonlinear Anal. 73(3), 788–795 (2010)
Li, G., Yang, C.: The existence of a nontrivial solution to a nonlinear elliptic boundary value problem of $$p$$ p -Laplacian type without the Ambrosetti–Rabinowitz condition. Nonlinear Anal. TMA 72, 4602–4613 (2010)
Miyagaki, O.H., Souto, M.A.: Superlinear problems without Ambrosetti and Rabinowitz growth condition. J. Diff. Equ. 245, 3628–3638 (2008)
Schechter, M.: The use of cerami sequences in critical point theory. Abstract and applied analysis (2007) (Article ID 58948)
Sun, M.Z.: Multiple solutions of a superlinear $$p$$ p -Laplacian equation without AR-condition. Appl. Anal. 89, 325–336 (2010)
Wang, J., Tang, C.L.: Existence and multiplicity of solutions for a class of superlinear $$p$$ p -Laplacian equations. Bound. Value Probl. 2006, 1–12 (2006)