Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn

• Autorzy: Bachar Imed , Mâagli Habib , Eltayeb Hassan

Identyfikatory

DOI

10.7494/OpMath.2022.42.6.793

• Języki publikacji: EN

Abstrakty

EN

In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of Rn (n ≥ 2). The global behavior of this solution is also given.

Słowa kluczowe

EN

nonnegative solution; semipositone; Kato class; fixed point theorem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2022
• Tom: Vol. 42, no. 6
• Strony: 793--803
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Bachar Imed

• King Saud University College of Science, Mathematics Department, P.O. Box 2455, Riyadh 11451, Saudi Arabia

• https://orcid.org/0000-0003-3808-5786

autor

Mâagli Habib

• King Abdulaziz University, College of Sciences and Arts, Rabigh Campus, Department of Mathematics, P.O. Box 344, Rabigh 21911, Saudi Arabia

• https://orcid.org/0000-0002-7977-8039

autor

Eltayeb Hassan

• King Saud University College of Science, Mathematics Department, P.O. Box 2455, Riyadh 11451, Saudi Arabia

• https://orcid.org/0000-0003-1820-9921

Bibliografia

• [1] G.A. Afrouzi, S.H. Rasouli, On positive solutions for some nonlinear semipositone elliptic boundary value problems, Nonlinear Anal. Model. Control 11 (2006), no. 4, 323–329.
• [2] V. Anuradha, D.D. Hai, R. Shivaji, Existence results for superlinear semipositone BVP’s, Proc. Amer. Math. Soc. 124 (1996), no. 3, 757–763.
• [3] R. Aris, Introduction to the Analysis of Chemical Reactors, Prentice Hall, New Jersey, 1965.
• [4] M. Bełdziński, M. Galewski, On solvability of elliptic boundary value problems via global invertibility, Opuscula Math. 40 (2020), no. 1, 37–47.
• [5] K.J. Brown, R. Shivaji, Simple proofs of some results in perturbed bifurcation theory, Proc. Roy. Soc. Edinburgh Sect. A 93 (1982), no. 1–2, 71–82.
• [6] A. Castro, R. Shivaji, Nonnegative solutions for a class of nonpositone problems, Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), no. 3–4, 291–302.
• [7] K.L. Chung, Z. Zhao, From Brownian Motion to Schrödinger’s Equation, Springer-Verlag, 1995.
• [8] G. Figueiredo, V.D. Rădulescu, Nonhomogeneous equations with critical exponential growth and lack of compactness, Opuscula Math. 40 (2020), no. 1, 71–92.
• [9] J.R. Graef, L. Kong, Positive solutions for third order semipositone boundary value problems, Appl. Math. Lett. 22 (2009), no. 8, 1154–1160.
• [10] M. Ghergu, V.D. Rădulescu, Sublinear singular elliptic problems with two parameters, J. Differential Equations 195 (2003), no. 2, 520–536.
• [11] P.-L. Lions, On the existence of positive solutions of semilinear elliptic equations, SIAM Rev. 24 (1982), no. 4, 441–467.
• [12] R. Ma, S. Wang, Positive solutions for some semi-positone problems with nonlinear boundary conditions via bifurcation theory, Mediterr. J. Math. 17 (2020), Article no. 12.
• [13] H. Mâagli, Asymptotic behavior of positive solutions of a semilinear Dirichlet problem, Nonlinear Anal. 74 (2011), no. 9, 2941–2947.
• [14] H. Mâagli, L. Mâatoug, Singular solutions of a nonlinear equation in bounded domains of R2, J. Math. Anal. Appl. 270 (2002), 230–246.
• [15] H. Mâagli, M. Zribi, On a new Kato class and singular solutions of a nonlinear elliptic equation in bounded domain of Rn, Positivity 9 (2005), no. 4, 667–686.
• [16] N.S. Papageorgiou, Double phase problems: a survey of some recent results, Opuscula Math. 42 (2022), no. 2, 257–278.
• [17] N.S. Papageorgiou, V.D. Rădulescu, D.D. Repovš, Existence and multiplicity of solutions for double-phase Robin problems, Bull. Lond. Math. Soc. 52 (2020), no. 3, 546–560.
• [18] S.C. Port, C.J. Stone, Brownian Motion and Classical Potential Theory, Academic Press, San Diego, 1978.
• [19] V.D. Rădulescu, Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations: Monotonicity, Analytic, and Variational Methods, Contemporary Mathematics and its Applications, 6. Hindawi Publishing Corporation, 2008.
• [20] M. Selmi, Inequalities for Green functions in a Dini–Jordan domain in R2, Potential. Anal. 13 (2000), no. 1, 81–102.
• [21] F. Toumi, Existence of positive solutions for nonlinear boundary-value problems in bounded domains of Rn, Abstr. Appl. Anal. 2006 (2006), Article ID 95480.
• [22] J. Zhang, W. Zhang, V.D. Rădulescu, Double phase problems with competing potentials: concentration and multiplication of ground states, Math. Z. 301 (2022), no. 4, 4037–4078.
• [23] X. Zhang, L. Liu, Y. Wu, Positive solutions of nonresonance semipositone singular Dirichlet boundary value problems, Nonlinear Anal. 68 (2008), no. 1, 97–108.
• [24] W. Zou, X. Li, Existence results for nonlinear degenerate elliptic equations with lower order terms, Adv. Nonlinear Anal. 10 (2021), no. 1, 301–310.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).