Existence and Uniqueness Results for Some Nonlinear Boundary Value Problems

Hai, D. D.; Oppenheimer, Seth F.

doi:10.1006/jmaa.1996.0066

Cited by 65 publications

(39 citation statements)

References 5 publications

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“…Finally for both cases dom A = R N and dom A = R N , we consider the 'nonconvex problem' (i.e. F does not need to have convex values, see hypotheses H(F) 3 and H(F) 4 ).…”

Section: Existence Theoremsmentioning

confidence: 99%

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Nonlinear second-order multivalued boundary value problems

Gasiński

Papageorgiou

2003

Proc. Math. Sci.

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Abstract. In this paper we study nonlinear second-order differential inclusions involving the ordinary vector p-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the 'convex' and 'nonconvex' problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.

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“…Finally for both cases dom A = R N and dom A = R N , we consider the 'nonconvex problem' (i.e. F does not need to have convex values, see hypotheses H(F) 3 and H(F) 4 ).…”

Section: Existence Theoremsmentioning

confidence: 99%

“…is a multifunction, which satisfies hypotheses H(F) 3 (i), (ii), (iii), but with a k ∈ L p ′ ([0, T ]) + and hypothesis H(F) 1 (iv). 2 , H(F) 4 and H(ξ ) hold, then problem (1.1) has a solution x ∈ C 1 ([0, T ]; R N ).…”

Section: Theorem 3 If Hypotheses H(mentioning

confidence: 99%

Nonlinear second-order multivalued boundary value problems

Gasiński

Papageorgiou

2003

Proc. Math. Sci.

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“…In addition our work is related to the recent papers which examine single-valued differential equations involving the one-dimensional p-Laplacian. We mention the work of Boccardo-Drábek-GiachettiKučera [2], Dang-Oppenheimer [7], Del Pino-Elgueta-Manasevich [8], Drábek [9], Fabry-Fayyad [14], Guo [19], Manasevich-Mawhin [28] and the references therein. All these papers (with the exception of Manasevich-Mawhin [28]) study scalar problems.…”

Section: Introductionmentioning

confidence: 99%

“…In Boccardo-Drábek-Giachetti-Kučera [2], Del Pino-Elgueta-Manasevich [8], the boundary conditions are Dirichlet. In Fabry-Fayyad [14] and Manasevich-Mawhin [28] the authors investigate the periodic problem, while Guo [19] deals with both the periodic and the Neumann problems and finally Dang-Oppenheimer [7] examine all three problems (Dirichlet, Neumann and periodic). It should be mentioned here that Dang-Oppenheimer [7] and Manasevich-Mawhin [28] use a general p-Laplacianlike differential operator which is not necessarily homogeneous and has no growth restrictions.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Boundary Value Problems for Second Order Differential Inclusions

2005

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“…We refer to the works of Del Pino-Manasevich-Murua [5], Fabry-Fayyad [6], Guo [7], Dang-Oppenheimer [4] (scalar problems), and Manasevich-Mawhin [10], Mawhin [11], Kyritsi-MatzakosPapageorgiou [9] (vector problems). In all these works the method of analysis is based on degree theoretic arguments or on the theory of nonlinear operators of monotone type and on fixed point results (see Kyritsi-Matzakos-Papageorgiou [9]).…”

Section: Introductionmentioning

confidence: 99%