Existence of multiple solutions for some nonlinear boundary value problems

Nkashama, M. N.; Santanilla, Jairo

doi:10.1016/0022-0396(90)90131-8

Cited by 22 publications

(14 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We assume that f fulfils the Carathéodory conditions on The problem (0.2) was considered by M. N. Nkashama and J. Santanilla in [6], where a.o. the following three results concerning the existence of nonnegative and nonpositive solutions to the problem (0.…”

Section: Uoe=f(t U) U(0)=u(1) Uoe(0)=uoe(1) (02)mentioning

confidence: 99%

Existence of Nonnegative and Nonpositive Solutions for Second Order Periodic Boundary Value Problems

Rachůnková

Tvrdý

Vrkoč

2001

Journal of Differential Equations

121

View full text Add to dashboard Cite

We are interested in nonnegative and nonpositive solutions of the boundary value problem uoe=f (t, u), u(0)=u(1), uOE(0)=uOE (1), where f fulfils the Carathéodory conditions on [0, 1] × R. We generalize the results reached by M. N. Nkashama, J. Santanilla and L. Sanchez and present estimates for solutions. In addition, we apply our existence theorems to periodic boundary value problems for nonlinear Duffing equations whose right-hand sides have a repulsive or attractive singularity at the origin. We extend or generalize existence results by A. C. Lazer and S. Solimini and other authors. Moreover, we get some multiplicity results and in the case of a repulsive singularity we also admit a weak singularity, in constrast to the previous papers on this subject. Our proofs are based on the method of lower and upper functions and topological degree arguments and the results are tested on examples.

show abstract

Section: Uoe=f(t U) U(0)=u(1) Uoe(0)=uoe(1) (02)mentioning

confidence: 99%

Existence of Nonnegative and Nonpositive Solutions for Second Order Periodic Boundary Value Problems

Rachůnková

Tvrdý

Vrkoč

2001

Journal of Differential Equations

121

View full text Add to dashboard Cite

show abstract

“…By (d1) and Theorem 3.1, we assert that the problem (P) has at least one positive solution u * ∈ K . The proof of (2) is similar to (1). (3) and (4) are derived from (1) and (2) by applying Lemma 4.2, respectively.…”

Section: On the Limit Casesmentioning

confidence: 96%

“…Moreover, the conditions (a1)-(a3) imply that the problem (P) may be singular or nonsingular. Because of wide interests in physics and engineering, second-order periodic boundary value problems have been investigated by many authors (see [1][2][3][4][5][6]). In most real problems, only the positive solution is significant.…”

Section: Introductionmentioning

confidence: 99%

Positive solutions of nonlinear second-order periodic boundary value problems

Qing-liu

2007

Applied Mathematics Letters

View full text Add to dashboard Cite

show abstract

“…(1.2) Due to a wide range of applications in physics and engineering, second order periodic boundary value problems have been investigated by many authors [1][2][3][4][5][6][7][8][9][10]. When a(t) ≡ 0 and ω = 2π , in [11], Yao obtained the conditions for the existence of single positive solution and multiple positive solutions for the following PBVP…”

Section: Introductionmentioning

confidence: 97%

Existence of nontrivial periodic solutions for a nonlinear second order periodic boundary value problem

Liu

2010

Nonlinear Analysis: Theory, Methods & Applications

View full text Add to dashboard Cite

Existence of multiple solutions for some nonlinear boundary value problems

Cited by 22 publications

References 9 publications

Existence of Nonnegative and Nonpositive Solutions for Second Order Periodic Boundary Value Problems

Existence of Nonnegative and Nonpositive Solutions for Second Order Periodic Boundary Value Problems

Positive solutions of nonlinear second-order periodic boundary value problems

Existence of nontrivial periodic solutions for a nonlinear second order periodic boundary value problem

Contact Info

Product

Resources

About