Existence and Multiplicity of Solutions for Fractional Elliptic Problems with Discontinuous Nonlinearities
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DOI: 10.1007/s00009-018-1188-7
Abstract: We consider the following fractional elliptic problem: $$\begin{aligned} (P)\left\{ \begin{array}{ll} (-\Delta )^s u = f(u) H(u-\mu )&{} \quad \text{ in } \ \Omega ,\\ u =0 &{}\quad \text{ on } \ \mathbb{{R}}^n {\setminus } \Omega… read more here.
Keywords: multiplicity solutions; existence multiplicity; solutions fractional; fractional elliptic ... See more keywords
Multiplicity of solutions for elliptic equations involving fractional operator and sign-changing nonlinearity
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DOI: 10.1007/s11868-020-00357-9
Abstract: In this work, we study the existence and the multiplicity of non-negative solutions for the following problem $$\begin{aligned} ({\mathrm{P}}_\uplambda ) \left\{ \begin{array}{ll} \mathcal {L} u = a(x) u^{q}+ \lambda b(x) u^p\quad \text {in }\Omega ,… read more here.
Keywords: multiplicity; lambda; multiplicity solutions; elliptic equations ... See more keywords
Multiplicity of solutions for a nonlocal nonhomogeneous elliptic equation with critical exponential growth
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.03.039
Abstract: Abstract In this paper we are interested in the following nonlocal nonhomogeneous elliptic equation in R 2 , − Δ u + V ( x ) u = ( 1 | x | μ ⁎… read more here.
Keywords: multiplicity solutions; nonhomogeneous elliptic; exponential growth; elliptic equation ... See more keywords
Existence and multiplicity of solutions for Dirichlet problem of p(x)-Laplacian type without the Ambrosetti-Rabinowitz condition
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DOI: 10.1016/j.jmaa.2020.123882
Abstract: Abstract This paper deals with the following variational problem with variable exponents { − div ( ( 1 + | ∇ u | p ( x ) 1 + | ∇ u | 2 p… read more here.
Keywords: multiplicity solutions; existence multiplicity; ambrosetti rabinowitz; condition ... See more keywords
Existence and multiplicity of solutions for Kirchhoff-type potential systems with variable critical growth exponent
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DOI: 10.1080/00036811.2021.1979223
Abstract: In this paper, by using the concentration-compactness principle of Lions for variable exponents found in [Bonder JF, Silva A. Concentration-compactness principal for variable exponent space and app... read more here.
Keywords: multiplicity solutions; existence multiplicity; type potential; solutions kirchhoff ... See more keywords
Existence and multiplicity of solutions for a supercritical elliptic problem in unbounded cylinders
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DOI: 10.1186/s13661-017-0783-z
Abstract: AbstractWe consider the following elliptic problem: {−div(|∇u|p−2∇u|y|ap)=|u|q−2u|y|bq+f(x)in Ω,u=0on ∂Ω,$$ \textstyle\begin{cases} -\operatorname{div} ( \frac{ \vert \nabla u \vert ^{p-2} \nabla u}{ \vert y \vert ^{ap}} ) = \frac { \vert u \vert ^{q-2} u}{ \vert y \vert ^{bq}}… read more here.
Keywords: multiplicity solutions; existence multiplicity; elliptic problem; vert ... See more keywords
Potential well and multiplicity of solutions for nonlinear Dirac equations
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DOI: 10.3934/cpaa.2020028
Abstract: In this paper we consider the semi-classical solutions of a massive Dirac equations in presence of a critical growth nonlinearity \begin{document}$ -i\hbar \sum\limits_{k = 1}^{3}\alpha_k\partial_k w+a\beta w+V(x)w = f(|w|)w. $\end{document} Under a local condition imposed… read more here.
Keywords: nonlinear dirac; multiplicity solutions; dirac equations; potential well ... See more keywords