Abstract
Applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of positive radial solutions for some second-order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.
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References
Lions P L. On the existence of positive solutions of semilinear elliptic equations[J].SIAM Rev, 1982,24(4):441–467.
NI Wei-ming, Nussbanm R D. Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r)=0[J].Comm Pure Appl Math, 1985,38(1):67–108.
Bandle C, Coffman CV, Marcus M. Nonlinear elliptic problems in annular domains[J].J Differential Equations, 1987,69(3):322–345.
LIN Song-sun. On the existence of positive radial solutions for nonlinear elliptic equations in annular domains[J].J Differential Equations, 1989,81(2):221–233.
WANG Hai-yan. On the existence of positive solutions for semilinear elliptic equations in annulus [J].J Differential Equations, 1994,109(1):1–7.
Erbe L H, HU Shou-chuan, WANG Hai-yan. Multiple positive solutions of some boundary value problems[J].J Math Anal Appl, 1994,184(3):640–648.
YAO Qing-liu, BAI Zhang-bing. Existence of Positive solutions of BVP foru (4) (t)−λh(t)f(u(t))=0[J].Chinese Annals of Math, Ser A, 2000,20(5):575–578. (in Chinese)
YAO Qing-liu. Existence of positive radial solutions of Dirichlet problems for elliptic equations Δu+g(|X|)f(u)=0 in annulus[J].Acta Mathematica Scientica, Ser A, 2002,20(3):414–418. (in Chinese)
YAO Qing-liu, WANG Jing-rong. Multiple positive radial solutions of Dirichlet problems for elliptic equations Δu+g(|X|)f(u)=0 in annulus[J].Systems Science and Mathematical Sciences, 2000,20 (4):487–492. (in Chinese)
YAO Qing-liu. Positive solutions for generalized Gelfand models[J].Appl Math J Chinese Univ, Ser A, 2001,16(4):407–413. (in Chinese)
YAO Qing-liu. Positive solution of a class of singular sublinear two-point boundary value problems[J].Acta Mathematicae Applicatae Sinica, 2001,24(4):522–526. (in Chinese)
ZHONG Cheng-kui, FAN Xian-ling, CHEN Wen-yuan.Introduction to Nonlinear Functional Analysis [M]. Lanzhou: Lanzhou University Press, 1998, 143–154. (in Chinese)
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Communicated by Lin Zong-chi
Biography: Yao Qing-liu (1946-)
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Qing-liu, Y., Qin-sheng, M. Existence of positive radial solutions for some semilinear elliptic equations in annulus. Appl Math Mech 23, 1452–1457 (2002). https://doi.org/10.1007/BF02438385
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DOI: https://doi.org/10.1007/BF02438385