Existence of positive solutions for n+2 order p-Laplacian BVP

Authors:
Shiueh-Ling Yu;Fu-Hsiang Wong;Cheh-Chih Yeh;Shang-Wen Lin
Affiliations:
Holistic Education Centre, St John's University, Tamsui, Taipei, Taiwan, ROC;Department of Mathematics, National Taipei University of Education, 134, Ho-Ping E. Rd, Sec2, Taipei 10659, Taiwan, ROC;Department of Information Management, Lunghwa University of Science and Technology, Kueishan Taoyuan, 333, Taiwan, ROC;Department of Mathematics, Tamkang University, 151 Ying-chuan Road, Tamsui, Taipei County, 25137, Taiwan, ROC
Venue:
Computers & Mathematics with Applications
Year:
2007

Citing 5
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Abstract

Under some suitable assumptions, we show that the n+2 order non-linear boundary value problems (BVP"1){(E"1)[@f"p(u^(^n^)(t))]^''=f(t,u(t),u^(^1^)(t),...,u^(^n^+^1^)(t))(BC"1){u^(^i^)(0)=0,i=0,1,2,...,n-3,u^(^n^-^1^)(1)=0u^(^n^-^2^)(0)=@lu^(^n^-^1^)(@h)u^(^n^+^1^)(0)=@a"1u^(^n^+^1^)(@x)u^(^n^)(1)=@b"1u^(^n^)(@x) and (BVP"2){(E"2)[@f"p(u^(^n^)(t))]^''=f(t,u(t),u^(^1^)(t),...,u^(^n^+^1^)(t))(BC"2){u^(^i^)(0)=0,i=0,1,2,...,n-3,u^(^n^-^1^)(0)=0u^(^n^-^2^)(1)=-@lu^(^n^-^1^)(@h)u^(^n^+^1^)(0)=@a"1u^(^n^+^1^)(@x)u^(^n^)(1)=@b"1u^(^n^)(@x) have at least two positive solutions in C^n[0,1].