## Abstract

By variational and topological methods we prove the existence of a positive interval {Lambda} such that for all {lambda} {epsilon} {Lambda} there exists at least three positive solutions of (1.1) on {Omega} = D{sub R} {l_brace}(x,y) {epsilon} R{sup 2}{sub +}: x{sup 2} + y{sup 2} < R{sup 2}{r_brace}, where f: R {yields} R is a function of type (t{sup {sigma}}-t{sup {sigma}+{alpha}}){sub {chi}(0,1)}(t) with {sigma} > 1 and {alpha} {<=} 1, h is a non negative bounded smooth function. Under some restrictions for f and h we show that {Lambda} is independent of R, for R big enough. This type of problem arises in an astrophysical gravity free model of solar flares given by Heyvaerts et al. (author). 9 refs.

## Citation Formats

Calahorrano, M, and Dobarro, F.
Multiple solutions for inhomogeneous elliptic problems arising in astrophysics.
IAEA: N. p.,
1991.
Web.

Calahorrano, M, & Dobarro, F.
Multiple solutions for inhomogeneous elliptic problems arising in astrophysics.
IAEA.

Calahorrano, M, and Dobarro, F.
1991.
"Multiple solutions for inhomogeneous elliptic problems arising in astrophysics."
IAEA.

@misc{etde_10105548,

title = {Multiple solutions for inhomogeneous elliptic problems arising in astrophysics}

author = {Calahorrano, M, and Dobarro, F}

abstractNote = {By variational and topological methods we prove the existence of a positive interval {Lambda} such that for all {lambda} {epsilon} {Lambda} there exists at least three positive solutions of (1.1) on {Omega} = D{sub R} {l_brace}(x,y) {epsilon} R{sup 2}{sub +}: x{sup 2} + y{sup 2} < R{sup 2}{r_brace}, where f: R {yields} R is a function of type (t{sup {sigma}}-t{sup {sigma}+{alpha}}){sub {chi}(0,1)}(t) with {sigma} > 1 and {alpha} {<=} 1, h is a non negative bounded smooth function. Under some restrictions for f and h we show that {Lambda} is independent of R, for R big enough. This type of problem arises in an astrophysical gravity free model of solar flares given by Heyvaerts et al. (author). 9 refs.}

place = {IAEA}

year = {1991}

month = {Jul}

}

title = {Multiple solutions for inhomogeneous elliptic problems arising in astrophysics}

author = {Calahorrano, M, and Dobarro, F}

abstractNote = {By variational and topological methods we prove the existence of a positive interval {Lambda} such that for all {lambda} {epsilon} {Lambda} there exists at least three positive solutions of (1.1) on {Omega} = D{sub R} {l_brace}(x,y) {epsilon} R{sup 2}{sub +}: x{sup 2} + y{sup 2} < R{sup 2}{r_brace}, where f: R {yields} R is a function of type (t{sup {sigma}}-t{sup {sigma}+{alpha}}){sub {chi}(0,1)}(t) with {sigma} > 1 and {alpha} {<=} 1, h is a non negative bounded smooth function. Under some restrictions for f and h we show that {Lambda} is independent of R, for R big enough. This type of problem arises in an astrophysical gravity free model of solar flares given by Heyvaerts et al. (author). 9 refs.}

place = {IAEA}

year = {1991}

month = {Jul}

}