Posts by Radu Precup

Radu Precup

Abstract


We are concerned with existence, localization and multiplicity of positive radial solutions to Dirichlet problems with φ-Laplacians in a ball, in both scalar and system cases. Our approach essentially relies on fixed point index computations and a main feature is that it avoids any Harnack type inequality. Applications to some problems involving operators with Uhlenbeck structure are discussed.

Authors

Petru Jebelean
Institute for Advanced Environmental Research, West University of Timişoara, Timişoara, Romania

Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Jorge Rodríguez-López
CITMAga & Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782, Facultade de Matemáticas, Campus Vida, Santiago, Spain

Keywords

Dirichlet problem; Operator with Uhlenbeck structure; Positive radial solution; Fixed point index; Mean curvature operator; p-Laplacian

Paper coordinates

P. Jebelean, R. Precup, J. Rodríguez-López, Positive radial solutions for Dirichlet problems in the ball, Nonlinear Analysis, 240 (2024), art. id. 113470, https://doi.org/10.1016/j.na.2023.113470

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Journal

Nonlinear Analysis

Publisher Name

Elsevier

DOI

https://doi.org/10.1016/j.na.2023.113470

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[1] Amann H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18 (1976), pp. 620-709,  
CrossRefView in ScopusGoogle Scholar
[2] Bereanu C., Jebelean P., Torres P.J., Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space J. Funct. Anal., 264 (2013), pp. 270-287, View PDFView articleView in ScopusGoogle Scholar
[3] Candito P., Guarnotta U., Livrea R., Existence of two solutions for singular Φ-Laplacian problems, Adv. Nonlinear Stud., 22 (2022), pp. 659-683,   CrossRefView in ScopusGoogle Scholar
[4] Cheng X., Lü H., Multiplicity of positive solutions for a (p1,p2)– Laplacian system and its applications, Nonlinear Anal. RWA, 13 (2012), pp. 2375-2390
View PDFView articleView in ScopusGoogle Scholar
[5] Corrêa F.J.S.A., Carvalho M.L., Gonçalves J.V.A., Silva K.O., Positive solutions of strongly nonlinear elliptic problems, Asymptot. Anal., 93 (2015), pp. 1-20
View in ScopusGoogle Scholar
[6] Dalmasso R., Existence of positive radial solutions for a semilinear elliptic system without variational structure, Nonlinear Anal., 67 (2007), pp. 1255-1259
View PDFView articleView in ScopusGoogle Scholar
[7] Drábek P., García-Huidobro M., Manásevich R., Positive solutions for a class of equations with a p-Laplace like operator and weights Nonlinear Anal., 71 (2009), pp. 1281-1300View PDFView articleView in ScopusGoogle Scholar
[8] García-Huidobro M., Manásevich R., Schmitt K., Positive radial solutions of quasilinear elliptic partial differential equations on a ball Nonlinear Anal., 35 (1999), pp. 175-190, View PDFView articleView in ScopusGoogle Scholar
[9] García-Huidobro M., Manásevich R., Ubilla P., Existence of positive solutions for some Dirichlet problems with an asymptotically homogeneous operator, Electron. J. Differential Equations, 1995 (1995), pp. 1-22Google Scholar
[10] García-Huidobro M., Manásevich R., Zanolin F., Infinitely many solutions for a Dirichlet problem with a nonhomogeneous p-Laplacian-like operator in a ball, Adv. Differential Equations, 2 (1997), pp. 203-230View in ScopusGoogle Scholar

[11] Granas A., Dugundji J., Fixed Point Theory, Springer-Verlag, New York (2003), Google Scholar
[12] Guo D., Lakshmikantham V., Nonlinear Problems in Abstract Cones, Academic Press, San Diego (1988), Google Scholar
[13] Gurban D., Jebelean P., Positive radial solutions for systems with mean curvature operator in Minkowski space, Rend. Istit. Mat. Univ. Trieste, 49 (2017), pp. 245-264, View in ScopusGoogle Scholar
[14] Gurban D., Jebelean P., Positive radial solutions for multiparameter Dirichlet systems with mean curvature operator in Minkowski space and Lane–Emden type nonlinearities, J. Differential Equations, 266 (2019), pp. 5377-5396, View PDFView articleView in ScopusGoogle Scholar
[15] Lee Y.-H., Existence of multiple positive radial solutions for a semilinear elliptic system on an unbounded domain, Nonlinear Anal., 47 (2001), pp. 3649-3660, View PDFView articleView in ScopusGoogle Scholar
[16] Precup R., A vector version of Krasnosel’skiĭ’s fixed point theorem in cones and positive periodic solutions of nonlinear systems, J. Fixed Point Theory Appl., 2 (2007), pp. 141-151, View article, CrossRefView in ScopusGoogle Scholar
[17] Precup R., Rodríguez-López J., Multiplicity results for operator systems via fixed point index, Results Math., 74 (2019), pp. 1-14, Google Scholar

[18] Precup R., Rodríguez-López J., Positive radial solutions for Dirichlet problems via a Harnack-type inequality, Math. Methods Appl. Sci. (2022), pp. 1-14, 10.1002/mma.8682, View PDF , This article is free to access, Google Scholar
[19] Rodríguez-López J., A fixed point index approach to Krasnosel’skiĭ–Precup fixed point theorem in cones and applications, Nonlinear Anal., 226 (113138) (2023), p. 19, Google Scholar
[20] Uhlenbeck K, Regularity for a class of non-linear elliptic systems, Acta Math., 138 (1977), pp. 219-240, View in ScopusGoogle Scholar
[21] Walter W., Differential and Integral Inequalities, Springer-Verlag, New York (1970), Google Scholar
[22] Zou H., A priori estimates for a semilinear elliptic system without variational structure and their applications, Math. Ann., 323 (2002), pp. 713-735, View in ScopusGoogle Scholar

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