A semilinear elliptic boundary value problem at resonance where the nonlinearity may grow linearly

Rumbos, Adolfo J.

doi:10.1016/0362-546x(91)90203-d

Cited by 16 publications

(10 citation statements)

References 4 publications

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“…However, it would have little practical value unless more easily computed solvability conditions could be derived as corollaries. Fortunately, this is indeed the case as has been demonstrated in [16], [17] and [19].…”

Section: Proof We Already Knew Thatmentioning

confidence: 52%

Resonance and Nonresonance in Terms of Average Values

Nkashama

Robinson

1996

Journal of Differential Equations

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We prove existence results for nonlinear two-point boundary value problems. What sets our results apart is that we impose sufficient conditions for solvability in terms of the (asymptotic) average values of the nonlinearities. Our solvability conditions allow the nonlinear term to have significant oscillations outside the given spectral gap as long as it remains within the interval on the average in some sense.

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Section: Proof We Already Knew Thatmentioning

confidence: 52%

Resonance and Nonresonance in Terms of Average Values

Nkashama

Robinson

1996

Journal of Differential Equations

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“…The purpose of our discussion is to show that many well-known, and several new, existence theorems can be understood as simple corollaries of abstract existence theorems similar to those in [30] and [28]. This point of view is similar to that of L. Cesari, see for example [5] or [6], and of J. Mawhin, see for example [25], and in some respects our results can be viewed as an extension of their unifying work.…”

Section: Introductionmentioning

confidence: 72%

A general approach to solvability conditions for semilinear elliptic boundary value problems at resonance

Robinson¹,

Landesman²

1995

Differential Integral Equations

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“…However, it would have little practical value unless more easily computed solvability conditions could be derived as corollaries. Fortunately, this is indeed the case, as has been demonstrated in [19,20,22]. In our next theorem, we prove that an`averaged' version of the well-known Landesman{ Lazer condition, see [14], is su¯cient for the solvability of problem (1.1).…”

Section: Existence Theoremsmentioning

confidence: 81%

Resonance and non-resonance in terms of average values. II

Nkashama¹,

Robinson²

2001

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We prove existence results for semilinear elliptic boundary-value problems in both the resonance and non-resonance cases. What sets our results apart is that we impose su± cient conditions for solvability in terms of the (asymptotic) average values of the nonlinearities, thus allowing the nonlinear term to have signi¯cant oscillations outside the given spectral gap as long as it remains within the interval on the average in some sense. This work generalizes the results of a previous paper, which dealt exclusively with the ordinary di® erential equation (ODE) case and relied on ODE techniques.

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A semilinear elliptic boundary value problem at resonance where the nonlinearity may grow linearly

Cited by 16 publications

References 4 publications

Resonance and Nonresonance in Terms of Average Values

Resonance and Nonresonance in Terms of Average Values

A general approach to solvability conditions for semilinear elliptic boundary value problems at resonance

Resonance and non-resonance in terms of average values. II

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