On non-local nonlinear elliptic equations involving an eigenvalue problem View Full Text


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Article Info

DATE

2021-11-29

AUTHORS

Ching-yu Chen, Yueh-cheng Kuo, Kuan-Hsiang Wang, Tsung-fang Wu

ABSTRACT

The existence and multiplicity of solutions for a class of non-local elliptic boundary value problems with superlinear source functions are investigated in this paper. Using variational methods, we examine the changes arise in the solution behaviors as a result of the non-local effect. Comparisons are made of the results here with those of the elliptic boundary value problem in the absence of the non-local term under the same prescribed conditions to highlight this effect of non-locality on the solution behaviors. Our results here demonstrate that the complexity of the solution structures is significantly increased in the presence of the non-local effect with the possibility ranging from no permissible positive solution to three positive solutions and, contrary to those obtained in the absence of the non-local term, the solution profiles also vary depending on the superlinearity of the source functions. More... »

PAGES

45

References to SciGraph publications

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  • 1992-12. Global solvability for the degenerate Kirchhoff equation with real analytic data in INVENTIONES MATHEMATICAE
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  • 2016-01-04. Extinction for a discrete competition system with the effect of toxic substances in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2017-07-10. Ground state solutions of Nehari–Pohozaev type for Kirchhoff-type problems with general potentials in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 1993-10. On semilinear elliptic equations with indefinite nonlinearities in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 1990. Convexity Methods in Hamiltonian Mechanics in NONE
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    http://scigraph.springernature.com/pub.10.1007/s13398-021-01190-5

    DOI

    http://dx.doi.org/10.1007/s13398-021-01190-5

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