Existence and multiplicity results for some nonlinear problems with singular phi-Laplacian

By C. Bereanu, Jean Mawhin. 2007

183 citations recorded by the source corpus.

Using Leray-Schauder degree theory we obtain various existence and multiplicity results for nonlinear boundary value problems (phi(u'))' = f (t, u, u'), l(u, u') = 0 where l(u, u') = 0 denotes the Dirichlet, periodic or Neumann boundary conditions on [0, T], phi:]-a, a[ --> R is an increasing homeomorphism, phi(0) = 0. The Difichlet problem is always solvable. For Neumann or periodic boundary conditions, we obtain in particular existence conditions for nonlinearities which satisfy some sign conditions, upper and lower solutions theorems, Ambrosetti-Prodi type results. We prove Lazer-Solimini type results for singular nonlinearities and periodic boundary conditions. (C) 2007 Elsevier Inc. All rights reserved.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ae49bf0b6013b524f9b0fab4ff8923d7b2bb4b12

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In Applied Mathematics

1. Petru Jebelean
2. C. Bereanu
3. Jean Mawhin
4. Pedro J. Torres

In Mathematical Physics

1. Petru Jebelean
2. C. Bereanu
3. Jean Mawhin

Citations in the corpus

• Radial solutions for some nonlinear problems involving mean curvature operators in Euclidean and Minkowski spaces (2008, background): “The case where N = 1 was already considered in [3].”
• Radial solutions for Neumann problems involving mean curvature operators in Euclidean and Minkowski spaces (2010, methodology): “Remark 2 In the particular case N = 1 Theorem 1 was proved in [5], while Theorems 2 and 3 were obtained in [4].”
• Periodic Solutions of Pendulum-Like Perturbations of Singular and Bounded $${\phi}$$-Laplacians (2010, methodology): “Then we show in Theorem 2, using again degree arguments and the upper and lower solutions method developed in [2], that equation (2) has at least two solutions not differing by a multiple of 2π if ||h||∞ < μ, and at least one solution exists if ||h||∞ = μ.”