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Existence and multiplicity results for a semilinear elliptic problem

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Abstract In this paper we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least five solutions when the range of the derivative of the… Click to show full abstract

Abstract In this paper we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We make extensive use of variational methods and characterizations of the local degree of critical points. Furthermore, uniqueness and qualitative properties of the solutions are investigated.

Keywords: results semilinear; elliptic problem; problem; semilinear elliptic; existence multiplicity; multiplicity results

Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2019

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