Giải pháp vô hướng không bằng không cho một lớp hệ thống elliptic với điều kiện biên phi địa phương trên miền hình nhẫn

Agarwal, R.P., O’Regan, D., Wong, P.J.Y.: Constant-Sign Solutions of Systems of Integral Equations, Springer, Cham (2013) Amann H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18, 620–709 (1976) Amster P., Maurette M.: An elliptic singular system with nonlocal boundary conditions. Nonlinear Anal. 75, 5815–5823 (2012) Beals R.: Nonlocal elliptic boundary value problems. Bull. Am. Math. Soc. 70, 693–696 (1964) Bitsadze A.V., Samarskiĭ A.A.: Some elementary generalizations of linear elliptic boundary value problems (Russian). Anal. Dokl. Akad. Nauk SSSR 185, 739–740 (1969) Browder F.: Non-local elliptic boundary value problems. Am. J. Math. 86, 735–750 (1964) Cabada, A., Infante, G., Tojo, F.A.F.: Nonzero solutions of perturbed Hammerstein integral equations with deviated arguments and applications. Topol. Methods Nonlinear Anal. (to appear, 2015) Cheng X., Zhang Z.: Existence of positive solutions to systems of nonlinear integral or differential equations. Topol. Methods Nonlinear Anal. 34, 267–277 (2009) Cheng X., Zhong C.: Existence of positive solutions for a second-order ordinary differential system. J. Math. Anal. Appl. 312, 14–23 (2005) Conti R.: Recent trends in the theory of boundary value problems for ordinary differential equations. Boll. Un. Mat. Ital. 22, 135–178 (1967) Dunninger D.R., Wang H.: Existence and multiplicity of positive solutions for elliptic systems. Nonlinear Anal. 29, 1051–1060 (1997) Dunninger D.R., Wang H.: Multiplicity of positive radial solutions for an elliptic system on an annulus. Nonlinear Anal. 42, 803–811 (2000) do Ó J.M., Lorca S., Ubilla P.: Local superlinearity for elliptic systems involving parameters. J. Differ. Equ. 211, 1–19 (2005) do Ó J.M., Lorca S., Ubilla P.: Three positive solutions for a class of elliptic systems in annular domains. Proc. Edinb. Math. Soc. 2(48), 365–373 (2005) do Ó J.M., Sánchez J., Lorca S., Ubilla P.: Positive solutions for a class of multiparameter ordinary elliptic systems. J. Math. Anal. Appl. 332, 1249–1266 (2007) Franco D., Infante G., O’Regan D.: Nontrivial solutions in abstract cones for Hammerstein integral systems. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 14, 837–850 (2007) Goodrich C.S.: Nonlocal systems of BVPs with asymptotically superlinear boundary conditions. Comment. Math. Univ. Carolin. 53, 79–97 (2012) Goodrich C.S.: Nonlocal systems of BVPs with asymptotically sublinear boundary conditions. Appl. Anal. Discrete Math. 6, 174–193 (2012) Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, Boston (1988) Henderson J., Luca R.: Existence and multiplicity for positive solutions of a system of higher-order multi-point boundary value problems. NoDEA Nonlinear Differ. Equ. Appl. 20, 1035–1054 (2013) Henderson J., Luca R.: Positive solutions for systems of second-order integral boundary value problems. Electron. J. Qual. Theory Differ. Equ. 70, 21 (2013) Infante G.: Eigenvalues of some non-local boundary-value problems. Proc. Edinb. Math. Soc. 46, 75–86 (2003) Infante G., Pietramala P.: Eigenvalues and non-negative solutions of a system with nonlocal BCs. Nonlinear Stud. 16, 187–196 (2009) Infante, G., Pietramala, P.: A cantilever equation with nonlinear boundary conditions Electron. J. Qual. Theory Differ. Equ. Spec. Ed. I, 15, 1–14 (2009) Infante G., Pietramala P.: Perturbed Hammerstein integral inclusions with solutions that change sign Comment. Math. Univ. Carolin. 50, 591–605 (2009) Infante G., Pietramala P.: Existence and multiplicity of non-negative solutions for systems of perturbed Hammerstein integral equations. Nonlinear Anal. 71, 1301–1310 (2009) Infante, G., Pietramala, P., Tojo, F.A.F.: Nontrivial solutions of local and non-local Neumann boundary value problems. Proc. R. Soc. Edinb. Sect. A. (to appear) Infante G., Webb J.R.L.: Nonzero solutions of Hammerstein integral equations with discontinuous kernels. J. Math. Anal. Appl. 272, 30–42 (2002) Infante G., Webb J.R.L.: Three point boundary value problems with solutions that change sign. J. Integral Equ. Appl. 15, 37–57 (2003) Karakostas G.L.: Existence of solutions for an n-dimensional operator equation and applications to BVPs. Electron. J. Differ. Equ. 71, 17 (2014) Krasnosel’skiĭ M.A., Zabreĭko P.P.: Geometrical Methods of Nonlinear Analysis. Springer, Berlin (1984) Lan K.Q.: Multiple positive solutions of Hammerstein integral equations with singularities. Differ. Equ. Dyn. Syst. 8, 175–195 (2000) Lan K.Q.: Multiple positive solutions of semilinear differential equations with singularities. J. Lond. Math. Soc. 63, 690–704 (2001) Lan K.Q., Lin W.: Multiple positive solutions of systems of Hammerstein integral equations with applications to fractional differential equations. J. Lond. Math. Soc. 83, 449–469 (2011) Lan K.Q., Lin W.: Positive solutions of systems of singular Hammerstein integral equations with applications to semilinear elliptic equations in annuli. Nonlinear Anal. 74, 7184–7197 (2011) Lan K.Q., Webb J.R.L.: Positive solutions of semilinear differential equations with singularities. J. Differ. Equ. 148, 407–421 (1998) Lee Y.-K.: Multiplicity of positive radial solutions for multiparameter semilinear elliptic systems on an annulus. J. Differ. Equ. 174, 420–441 (2001) Ma R.: Existence of positive radial solutions for elliptic systems. J. Math. Anal. Appl. 201, 375–386 (1996) Ma R.: A survey on nonlocal boundary value problems. Appl. Math. E-Notes 7, 257–279 (2001) Ntouyas, S.K.: Nonlocal initial and boundary value problems: a survey. Handbook of differential equations: ordinary differential equations. vol. II, pp. 461–557, Elsevier B. V., Amsterdam (2005) Picone M.: Su un problema al contorno nelle equazioni differenziali lineari ordinarie del secondo ordine. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 10, 1–95 (1908) Pietramala, P.: A note on a beam equation with nonlinear boundary conditions. Bound. Value Probl. Art. ID 376782 (2011) Precup, R.: Componentwise compression–expansion conditions for systems of nonlinear operator equations and applications. Mathematical models in engineering, biology and medicine. In: AIP Conference Proceedings, vol. 1124, pp. 284–293. American Institute of Physics, Melville (2009) Precup R.: Existence, localization and multiplicity results for positive radial solutions of semilinear elliptic systems. J. Math. Anal. Appl. 352, 48–56 (2009) Schechter M.: Nonlocal elliptic boundary value problems. Ann. Scuola Norm. Sup. Pisa. 20, 421–441 (1966) Skubachevskiĭ A.L.: Nonclassical boundary value problems. I. J. Math. Sci. (N. Y.). 155, 199–334 (2008) Skubachevskiĭ A.L.: Nonclassical boundary value problems. II. J. Math. Sci. (N. Y.). 166, 377–561 (2010) Štikonas A.: A survey on stationary problems, Green’s functions and spectrum of Sturm-Liouville problem with nonlocal boundary conditions. Nonlinear Anal. Model. Control 19, 301–334 (2014) Wang H.: On the existence of positive solutions for semilinear elliptic equations in the annulus. J. Differ. Equ. 109, 1–7 (1994) Wang Y.: Solutions to nonlinear elliptic equations with a nonlocal boundary condition. Electron. J. Differ. Equ. 05, 16 (2002) Webb J.R.L.: Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Anal. 47, 4319–4332 (2001) Webb, J.R.L.: Multiple positive solutions of some nonlinear heat flow problems. Discrete Contin. Dyn. Syst. Suppl. 895–903 (2005) Webb J.R.L.: Optimal constants in a nonlocal boundary value problem. Nonlinear Anal. 63, 672–685 (2005) Webb J.R.L.: Solutions of nonlinear equations in cones and positive linear operators. J. Lond. Math. Soc. 82, 420–436 (2010) Webb J.R.L.: A class of positive linear operators and applications to nonlinear boundary value problems. Topol. Methods Nonlinear Anal. 39, 221–242 (2012) Webb J.R.L., Infante G.: Positive solutions of nonlocal boundary value problems: a unified approach. J. Lond. Math. Soc. 74, 673–693 (2006) Webb J.R.L., Infante G.: Nonlocal boundary value problems of arbitrary order. J. Lond. Math. Soc. 79, 238–258 (2009) Webb J.R.L., Lan K.Q.: Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topol. Methods Nonlinear Anal. 27, 91–115 (2006) Whyburn W.M.: Differential equations with general boundary conditions. Bull. Am. Math. Soc. 48, 692–704 (1942) Yang Z.: Positive solutions to a system of second-order nonlocal boundary value problems. Nonlinear Anal. 62, 1251–1265 (2005) Yang Z.: Positive solutions for a system of nonlinear Hammerstein integral equations and applications. Appl. Math. Comput. 218, 11138–11150 (2012) Yang Z., Zhang Z.: Positive solutions for a system of nonlinear singular Hammerstein integral equations via nonnegative matrices and applications. Positivity 16, 783–800 (2012) Ye H., Ke Y.: A p-Laplace equation with nonlocal boundary condition in a perforated-like domain. Bull. Belg. Math. Soc. Simon Stevin 20, 895–908 (2013)