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This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the Kirchhoff typewhere Ω ⊂ R N , for N=1,2 and 3, is a bounded smooth domain, M and f are continuous functions and λ is a positive parameter. Our approach is based on the variational method.Mathematics subject classification (2010): 34B18, 34C11, 34K12, 35J25, 45M20.

No abstract

We study existence and multiplicity of solutions to the following bi‐nonlocal p(x)‐Kirchhoff equation via Krasnoselskii's genus, on the Sobolev space with variable exponent, MathClass-bin−M()MathClass-op∫Ω1p(x)MathClass-rel|MathClass-rel∇uMathClass-rel|p(x)Δp(x)uMathClass-rel=f(xMathClass-punc,u)[]MathClass-op∫ΩF(xMathClass-punc,u)r1emnbsp1emnbsp1emnbspin1emnbsp1emnbspΩMathClass-punc,1emnbsp1emnbsp1emnbspuMathClass-rel=01emnbsp1emnbspon1emnbsp1emnbsp∂ΩMathClass-punc, where Ω is a bounded smooth domain of I RN, 1 < p(x) < N, M and f are continuous functions, f is an odd function, F(xMathClass-punc,u)MathClass-rel=MathClass-op∫0uf(xMathClass-punc,ξ)dξ and r > 0 is a real parameter. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the p-Kirchhoff type and where Ω is a bounded smooth domain of ℝN, 1 < p < N, s ≥ p* = (pN)/(N – p) and M and f are continuous functions.