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.
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K.-H Wang was supported in part by the Ministry of Science and Technology, Taiwan (Grant No. 108-2811-M-390-500) and T.-F. Wu was supported in part by the Ministry of Science and Technology, Taiwan (Grant No. 108-2115-M-390-007-MY2).
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Chen, Cy., Kuo, Yc., Wang, KH. et al. On non-local nonlinear elliptic equations involving an eigenvalue problem. RACSAM 116, 45 (2022). https://doi.org/10.1007/s13398-021-01190-5
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DOI: https://doi.org/10.1007/s13398-021-01190-5