Drábek, Pavel; Girg, Petr; Roca, Francisco Remarks on the range properties of certain semilinear problems of Landesman-Lazer type. (English) Zbl 0993.34012 J. Math. Anal. Appl. 257, No. 1, 131-140 (2001). The authors consider the Dirichlet problem \[ u''(t)+ u(t)+ g(u'(t))= f(t),\quad u(0)= u(\pi)= 0. \] It is assumed that \(g\) is continuous, has finite limits \(g(+\infty)\), \(g(-\infty)\), and \(g(-\infty)< g(s)< g(+\infty)\) for all \(s\). The case of odd and increasing \(g\) with some asymptotic conditions is dealt with in more detail. The structure of the set of continuous functions \(f\) is studied for which the problem is solvable. Reviewer: Sergei A.Brykalov (Ekaterinburg) Cited in 1 ReviewCited in 4 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:Dirichlet problem; bounded nonlinearities × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Amann, H.; Ambrosetti, A.; Mancini, G., Elliptic equations with noninvertible Fredholm linear part and bounded nonlinearities, Math. Z., 158, 179-194 (1978) · Zbl 0368.35032 [2] Cañada, A.; Drábek, P., On semilinear problems with nonlinearities depending only on derivatives, SIAM J. Math. Anal., 27, 543-557 (1996) · Zbl 0852.34018 [3] Cañada, A.; Roca, F., Existence and multiplicity of solutions of some conservative pendulum-type equations with homogeneous Dirichlet conditions, Differential Integral Equations, 10, 1113-1122 (1997) · Zbl 0938.34013 [4] Fučı́k, S., Solvability of Nonlinear Equations and Boundary Value Problems (1980), Kluwer Academic: Kluwer Academic Dordrecht · Zbl 0453.47035 [5] Habets, P.; Sanchez, L., A two-point problem with nonlinearity depending only on the derivative, SIAM J. Math. Anal., 28, 1205-1211 (1997) · Zbl 0886.34015 [6] Kannan, R.; Nagle, R. K.; Pothoven, K. L., Remarks on the existence of solutions of \(x\)″+\(x\)+arctan \((x\)′)=\(p(t); x(0)=x\)(π)=0, Nonlinear Anal., 22, 793-796 (1994) · Zbl 0802.34021 [7] Landesman, E. M.; Lazer, A. C., Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Mat. Mech., 19, 609-623 (1970) · Zbl 0193.39203 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.