Existence of nonnegative solutions are established for the periodic problem y = f(t, y) a.e. on [0, T ], y(0) = y(T ). Here the nonlinearity f satisfies a Landesman Lazer type condition.

where the coefficients p,(t) are continuous functions on [0, a], pa(t) > 0, and the ah,, b, are constants. Our results show that, even for nonselfadjoint boundary value problems, a limited quantitative form of the Landesman and Lazer sufficient condition for existence holds. Moreover, further extensions are obtained of the recent form proposed by Shaw of the Landesman and Laxer theorem. The poi...

Abstract In this paper, we study the resonance problem of a class of singular quasilinear parabolic equations with respect to its higher near-eigenvalues. Under a generalized Landesman-Lazer condition, it is proved that the resonance problem admits at least one nontrivial solution in weighted Sobolev spaces. The proof is based upon applying the Galerkin-type technique, the Brouwer’s fixedpoint ...

Motivated by the problem of the existence of a solution of the nonlinear telegraph equation wt + clll u,, + h(t. c, u) = 0, such that u(t, ,) satisfies suitable boundary conditions over (0,~) ar;d Ilu(t,.)II is bounded over W for some function space norm 11 11: we prove the existence of bounded solutions over R of semilinear evolution equations in a Hilbert space of the form ii + cti + Au + g(t...

This paper surveys some recent results on the existence and multiplicity of periodic solutions of nonlinear difference equations of the first order under Ambrosetti-Prodi or Landesman-Lazer type conditions.

Sikiru Adigun Sanni Department of Mathematics and Statistics, University of Uyo, Akwa Ibom, 520003 Uyo, Nigeria Correspondence should be addressed to Sikiru Adigun Sanni, [email protected] Received 4 August 2011; Accepted 15 October 2011 Academic Editor: Yuji Liu Copyright q 2011 Sikiru Adigun Sanni. This is an open access article distributed under the Creative Commons Attribution License, ...

and Applied Analysis 3 B∞ There is h ∈ C Ω,R such that ∣∣f x, z ∣∣ ≤ h x , ∀ x, z ∈ Ω × R2, ∣∣g x, z ∣∣ ≤ h x , ∀ x, z ∈ Ω × R2. 1.8 Under these hypotheses, system 1.1 is asymptotically quadratic at infinity due to the presence of a linear part given by the function A ∈ S2 Ω . In addition, when λk A 1 for some k ≥ 1 the problem 1.1 becomes resonant. In this case, in order to obtain existence an...