# A note on solutions of semilinear equations at resonance in a cone

Annales Polonici Mathematici (1993)

- Volume: 58, Issue: 1, page 95-103
- ISSN: 0066-2216

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topBogdan Przeradzki. "A note on solutions of semilinear equations at resonance in a cone." Annales Polonici Mathematici 58.1 (1993): 95-103. <http://eudml.org/doc/262239>.

@article{BogdanPrzeradzki1993,

abstract = {A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).},

author = {Bogdan Przeradzki},

journal = {Annales Polonici Mathematici},

keywords = {nonnegative solutions; equations at resonance; semilinear problem; resonance; Landesman-Lazer type condition},

language = {eng},

number = {1},

pages = {95-103},

title = {A note on solutions of semilinear equations at resonance in a cone},

url = {http://eudml.org/doc/262239},

volume = {58},

year = {1993},

}

TY - JOUR

AU - Bogdan Przeradzki

TI - A note on solutions of semilinear equations at resonance in a cone

JO - Annales Polonici Mathematici

PY - 1993

VL - 58

IS - 1

SP - 95

EP - 103

AB - A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).

LA - eng

KW - nonnegative solutions; equations at resonance; semilinear problem; resonance; Landesman-Lazer type condition

UR - http://eudml.org/doc/262239

ER -

## References

top- [1] R. E. Gaines and J. Santanilla, A coincidence theorem in convex sets with applications to periodic solutions of ordinary differential equations, Rocky Mountain J. Math. 12 (1982), 669-678. Zbl0508.34030
- [2] E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623. Zbl0193.39203
- [3] J. L. Mawhin, Topological degree methods in nonlinear boundary value problems, CBMS Regional Conf. Ser. in Math. 40, Amer. Math. Soc., Providence, R.I., 1979.
- [4] B. Przeradzki, An abstract version of the resonance theorem, Ann. Polon. Math. 53 (1991), 35-43. Zbl0746.47043
- [5] B. Przeradzki, Operator equations at resonance with unbounded nonlinearities, preprint.
- [6] B. Przeradzki, A new continuation method for the study of nonlinear equations at resonance, J. Math. Anal. Appl., to appear.
- [7] J. Santanilla, Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential equations, ibid. 126 (1987), 397-408. Zbl0629.34017
- [8] J. Santanilla, Existence of nonnegative solutions of a semilinear equation at resonance with linear growth, Proc. Amer. Math. Soc. 105 (1989), 963-971. Zbl0687.47045
- [9] S. A. Williams, A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Differential Equations 8 (1970), 580-586. Zbl0209.13003

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