NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH#br# STRUM-LIOUVILLE BOUNDARY CONDITIONS

doi:10.1016/S0252-9602(11)60343-3

Abstract

Abstract:

This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C²ⁿ⁻²[0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C²ⁿ⁻¹[0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.

Key words: 2nth-order differential equation, singular boundary value problem, fixed point theorem, positive solution

CLC Number:

34B15

Cite this article

ZHAO Zeng-Qin. NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH#br# STRUM-LIOUVILLE BOUNDARY CONDITIONS[J].Acta mathematica scientia,Series B, 2011, 31(4): 1569-1582.

share this article

0
/ / Recommend

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(11)60343-3

http://121.43.60.238/sxwlxbB/EN/Y2011/V31/I4/1569

Trendmd

References

[1] Sun Hongrui, Li Wantong. Multiple positive solutions for even order Sturm-Liouville boundary value problems. Acta Math Sci, 2006, 26A(5): 700–706 (in Chinese)

[2] Yang Xiaojing. Existence of solutions for 2n-order boundary value problem. Appl Math Comput, 2003, 137: 77–87

[3] Zhao Zengqin. On the existence of positive solutions for 2n-order singular boundary value problems. Nonlinear Anal, TMA, 2006, 64: 2553–2561

[4] Sita Charkrit, Amnuay Kananthai, Existence of solutions for some higher order boundary value problems. J Math Anal Appl, 2007, 329: 830–850

[5] Zhang Xuemei, Feng Meiqiang, Positive solutions for a class of 2nth-order singular boundary value prob-lems. Nonlinear Anal, TMA, 2008, 69: 1287–1298

[6] Wei Zhongli, Pang Changci. A class of 2nth-order singular boundary value problems. Nonlinear Anal, TMA, 2007, 66: 1225–1245

[7] Liu Yuji. Note Solutions of two-point boundary value problems for even-order differential equations. J Math Anal Appl, 2006, 323: 721–740

[8] Yang Zhilin. Existence and uniqueness of positive solutions for a higher order boundary value problem. Comput Math Appl, 2007, 54: 220–228

[9] Liu Lishan, Zhang Xinguang, Wu Yonghong. Existence of positive solutions for singular higher-order differential equations. Nonlinear Anal, TMA, 2008, 68: 3948–3961

[10] Coster C De, Habets P. Two-Point Boundary Value Problems: Lower and Upper Solutions. Amsterdam: Elsevier, 2006

[11] Deimling K. Nonlinear Functional Analysis. New York: Springer-Verlag, 1985

[12] Guo Dajun. Nonlinear Functional Analysis. Jinan: Shandong Science and Technology Press, 2001 (in Chinese)

[13] Guo Dajun, Lakshmikantham V. Nonlinear Problems in Abstract Cones. Boston: Academic Press, 1988

Related Articles 15

[1]	Xiao ZHANG, Guoxing JI. SOLUTIONS TO THE SYSTEM OF OPERATOR EQUATIONS AXB=C=BXA [J]. Acta mathematica scientia,Series B, 2018, 38(4): 1143-1150.
[2]	Pengyan WANG, Yongzhong WANG. POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM [J]. Acta mathematica scientia,Series B, 2018, 38(3): 935-949.
[3]	Janusz BRZDȨK, Krzysztof CIEPLINSKI. ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS [J]. Acta mathematica scientia,Series B, 2018, 38(2): 377-390.
[4]	Jiafeng LIAO, Yang PU, Chunlei TANG. MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH [J]. Acta mathematica scientia,Series B, 2018, 38(2): 497-518.
[5]	Huifang JIA, Gongbao LI. MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N [J]. Acta mathematica scientia,Series B, 2018, 38(2): 391-418.
[6]	Wei SONG, Lin LI. CONTINUOUSLY DECREASING SOLUTIONS FOR A GENERAL ITERATIVE EQUATION [J]. Acta mathematica scientia,Series B, 2018, 38(1): 177-186.
[7]	Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ. ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION [J]. Acta mathematica scientia,Series B, 2017, 37(6): 1727-1739.
[8]	Ruyun MA, Hongliang GAO. MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF SEMIPOSITONE NEUMANN PROBLEMS WITH SINGULAR φ-LAPLACIAN [J]. Acta mathematica scientia,Series B, 2017, 37(5): 1472-1482.
[9]	Bashir AHMAD, Sotiris K. NTOUYAS, Jessada TARIBOON. A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS [J]. Acta mathematica scientia,Series B, 2016, 36(6): 1631-1640.
[10]	Yuji LIU. PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS [J]. Acta mathematica scientia,Series B, 2016, 36(5): 1492-1508.
[11]	Yan LI. NONEXISTENCE OF POSITIVE SOLUTIONS FOR A SEMI-LINEAR EQUATION INVOLVING THE FRACTIONAL LAPLACIAN IN R^N [J]. Acta mathematica scientia,Series B, 2016, 36(3): 666-682.
[12]	Adnène ARBI, Farouk CHÉRIF, Chaouki AOUITI, Abderrahmen TOUATI. DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS [J]. Acta mathematica scientia,Series B, 2016, 36(3): 891-912.
[13]	Anna BAHYRYCZ, Magdalena PISZCZEK. ON APPROXIMATELY (p, q)-WRIGHT AFFINE FUNCTIONS AND INNER PRODUCT SPACES [J]. Acta mathematica scientia,Series B, 2016, 36(2): 593-601.
[14]	A. AGHAJANI, M. MURSALEEN, A. SHOLE HAGHIGHI. FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS [J]. Acta mathematica scientia,Series B, 2015, 35(3): 552-566.
[15]	Xieping DING. EQUILIBRIUM EXISTENCE FOR MULTI-LEADER-FOLLOWER GENERALIZED CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY FC-UNIFORM SPACES [J]. Acta mathematica scientia,Series B, 2015, 35(2): 339-347.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	Yu Hongjun. GLOBAL CLASSICAL SOLUTIONS OF THE BOLTZMANN EQUATION NEAR MAXWELLIANS[J]. Acta mathematica scientia,Series B, 2006, 26(3): 491 -501 .
[2]	Ruan Lizhi; Zhang Jing. ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR HYPERBOLIC-ELLIPTIC COUPLED SYSTEM IN RADIATING GAS[J]. Acta mathematica scientia,Series B, 2007, 27(2): 347 -360 .
[3]	Zhen Jin; Ma Zhien; Han Maoan. GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS[J]. Acta mathematica scientia,Series B, 2006, 26(2): 291 -306 .
[4]	Lu Jianke. EXTENSION OF SOLUTIONS TO RIEMANN BOUNDARY VALUE PROBLEMS AND ITS APPLICATION[J]. Acta mathematica scientia,Series B, 2007, 27(4): 694 -702 .
[5]	Hakan Avci; A. Turan Gurkanli. MULTIPLIERS AND TENSOR PRODUCTS OF L(p, q) LORENTZ SPACES[J]. Acta mathematica scientia,Series B, 2007, 27(1): 107 -116 .
[6]	Wang Xia; Gao Fuqing. MODERATE DEVIATIONS FROM HYDRODYNAMIC LIMIT OF A GINZBURG-LANDAU MODEL[J]. Acta mathematica scientia,Series B, 2006, 26(4): 691 -701 .
[7]	Kong Linghai; Huan Zhongdan; Guo Boling. BV SOLUTIONS TO A DEGENERATE PARABOLIC EQUATION FOR IMAGE DENOISING[J]. Acta mathematica scientia,Series B, 2007, 27(1): 169 -179 .
[8]	Chen Liangyun; Meng Daoji. SOME RESULTS OF MODULAR LIE SUPERALGEBRAS[J]. Acta mathematica scientia,Series B, 2006, 26(3): 401 -409 .
[9]	Liu Youming. TWO CONDITIONS FOR NONUNIFORM GABOR FRAMES[J]. Acta mathematica scientia,Series B, 2006, 26(3): 415 -420 .
[10]	Liu Shaoping; Liao Xiaoxin. PERMANENCE AND PERSISTENCE OF TIME VARYING LOTKA-VOLTERRA SYSTEMS[J]. Acta mathematica scientia,Series B, 2006, 26(1): 49 -58 .

Abstract
References
Related Articles
Metrics
Comments
Recommended

TOP