On solutions of a fourth-order Lidstone boundary value problem at resonance

Jurkiewicz, Mariusz

doi:10.4064/ap95-1-1

Cited by 4 publications

(3 citation statements)

References 5 publications

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“…However, relatively little is known about the fourth-order problem at resonance; see Gupta et al [24,25], Jurkiewicz [26], and Iannacci and Nkashama [27]. The likely reason is that the spectrum theory of fourth-order operators is not available.…”

Section: Introductionmentioning

confidence: 99%

On a Fourth-Order Boundary Value Problem at Resonance

2017

Journal of Function Spaces

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We investigate the spectrum structure of the eigenvalue problem { (4) ( ) = ( ), ∈ (0, 1); (0) = (1) = (0) = (1) = 0}. As for the application of the spectrum structure, we show the existence of solutions of the fourth-order boundary value problem at resonance {− (4) ( ) + 1 ( ) + ( , ( )) = ℎ( ), ∈ (0, 1); (0) = (1) = (0) = (1) = 0}, which models a statically elastic beam with both end-points being cantilevered or fixed, where 1 is the first eigenvalue of the corresponding eigenvalue problem and nonlinearity may be unbounded.

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Section: Introductionmentioning

confidence: 99%

On a Fourth-Order Boundary Value Problem at Resonance

2017

Journal of Function Spaces

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“…It is seen that for some unions of lambdas, the differential operator that corresponds to the left-hand side of (1) is invertible and is not for others (see [4]). The second case, commonly called a resonance one, needs additional conditions of Landesman-Lazer type and was examined in [3], [4]. Here, we focus on the the nonresonant case.…”

Section: Introductionmentioning

confidence: 99%

“…[1,[4][5][6]9]). Most of the earlier discussions were devoted to the fourth order BVPs, for example see [3,7]. In this paper, we consider the depending on real parameters family of 2kth order (k ≥ 2) BVP,…”

Section: Introductionmentioning

confidence: 99%